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US11165535B2 - Polar code encoding method and apparatus in wireless communications - Google Patents

Polar code encoding method and apparatus in wireless communications Download PDF

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Publication number
US11165535B2
US11165535B2 US16/838,945 US202016838945A US11165535B2 US 11165535 B2 US11165535 B2 US 11165535B2 US 202016838945 A US202016838945 A US 202016838945A US 11165535 B2 US11165535 B2 US 11165535B2
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Prior art keywords
sequence
polarized channels
encoding
reliability
numbers
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US20200274642A1 (en
Inventor
Jun Wang
Gongzheng Zhang
Huazi Zhang
Chen Xu
Lingchen HUANG
Shengchen Dai
Hejia Luo
Yunfei Qiao
Rong Li
Jian Wang
Ying Chen
Nikita Polianskii
Mikhail Kamenev
Zukang Shen
Yourui HuangFu
Yinggang Du
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Huawei Technologies Co Ltd
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Huawei Technologies Co Ltd
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Priority claimed from CN201710653644.4A external-priority patent/CN107592181B/en
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Priority to US16/838,945 priority Critical patent/US11165535B2/en
Publication of US20200274642A1 publication Critical patent/US20200274642A1/en
Priority to US17/491,529 priority patent/US11811528B2/en
Application granted granted Critical
Publication of US11165535B2 publication Critical patent/US11165535B2/en
Priority to US18/485,303 priority patent/US12278702B2/en
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0056—Systems characterized by the type of code used
    • H04L1/0057—Block codes
    • H04L1/0058—Block-coded modulation
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/13—Linear codes
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0041—Arrangements at the transmitter end
    • H04L1/0043—Realisations of complexity reduction techniques, e.g. use of look-up tables
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0056—Systems characterized by the type of code used
    • H04L1/0057—Block codes
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0056—Systems characterized by the type of code used
    • H04L1/0061—Error detection codes
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/09—Error detection only, e.g. using cyclic redundancy check [CRC] codes or single parity bit
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/13—Linear codes
    • H03M13/134—Non-binary linear block codes not provided for otherwise
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/29—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes combining two or more codes or code structures, e.g. product codes, generalised product codes, concatenated codes, inner and outer codes
    • H03M13/2906—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes combining two or more codes or code structures, e.g. product codes, generalised product codes, concatenated codes, inner and outer codes using block codes

Definitions

  • Embodiments of this application relate to the field of communications technologies, and in particular, to a polar code encoding method and apparatus.
  • channel coding plays a key role in ensuring reliable transmission of data.
  • channel coding is usually performed by using a turbo code, a low-density parity-check (LDPC) code, and a polar code.
  • the turbo code cannot support information transmission at an excessively low or excessively high bit rate.
  • LDPC code Due to encoding/decoding characteristics of the turbo code and the LDPC code, it is very difficult for the turbo code and the LDPC code to achieve ideal performance in a case of a limited code length.
  • the turbo code and the LDPC code have relatively high computational complexity in an encoding/decoding implementation process.
  • the polar code is a good code that has been theoretically proved to be able to achieve the Shannon capacity and has relatively low encoding/decoding complexity, and therefore is more widely applied.
  • 5G communications systems will have some new characteristics.
  • eMBB enhanced mobile broadband
  • mMTC massive machine type communications
  • URLLC ultra-reliable and low-latency communications
  • the communications scenarios have higher requirements on encoding/decoding performance of the polar code.
  • Reliability ordering for polarized channels plays a key role in the encoding/decoding performance of the polar code.
  • accuracy of reliability ordering for polarized channels is not desirable, hindering further improvement of the encoding/decoding performance of the polar code during application.
  • Embodiments of this application provide a polar code encoding method and apparatus, to improve accuracy of reliability ordering for polarized channels.
  • a polar code encoding method includes: obtaining, by an encoding apparatus, to-be-encoded bits, where a length of the to-be-encoded bits is K, and K is a positive integer; obtaining a sequence used to encode the K to-be-encoded bits, where the sequence is denoted as a first sequence, the first sequence is used to represent an order of reliability of N polarized channels, the first sequence includes sequence numbers of the N polarized channels, the sequence numbers of the N polarized channels are arranged in the first sequence based on the reliability of the N polarized channels, N is a mother code length of a polar code, N is a positive integer power of 2, and K ⁇ N; selecting, in descending order of the reliability, the first K sequence numbers whose reliability rank relatively high in the first sequence; and mapping to-be-encoded information bits to polarized channels corresponding to the first K sequence numbers, and performing polar code encoding on the to-be-en
  • the first sequence is all of or a subset of a second sequence, where the second sequence includes sequence numbers of N max polarized channels, the sequence numbers of the N max polarized channels are arranged in the second sequence based on reliability of the N max polarized channels, N max is a positive integer, N max ⁇ N, and an order in which the sequence numbers of the polarized channels in the first sequence are arranged is consistent with an order in which sequence numbers less than N in the sequence numbers of the polarized channels in the second sequence are arranged.
  • the second sequence may be part or all of any sequence shown in Sequence Q1 to Sequence Q30 in the specification, the sequence numbers of the N polarized channels in the second sequence are arranged in ascending order of the reliability of the N polarized channels, and a minimum value of the sequence number of the polarized channel is 0.
  • the second sequence is part or all of any sequence shown in Table Q1 to Table Q30 in the specification the sequence numbers of the N polarized channels in the second sequence are arranged in ascending order of the reliability of the N polarized channels, and a minimum value of the sequence number of the polarized channel is 0.
  • the second sequence may be part or all of any sequence shown in Sequence Z1 to Sequence Z30 in the specification, each of the sequence numbers of the N polarized channels in the second sequence corresponds to the order of the reliability of the sequence number in the entire sequence, and a minimum value of the sequence number of the polarized channel is 0.
  • the second sequence is part or all of any sequence shown in Table Z1 to Table Z30 in the specification, each of the sequence numbers of the N polarized channels in the second sequence corresponds to the order of the reliability of the sequence number in the entire sequence, and a minimum value of the sequence number of the polarized channel is 0.
  • a polar code encoding apparatus has a function of implementing the method according to any one of the first aspect and the possible designs of the first aspect.
  • the function may be implemented by using hardware, or may be implemented by using hardware to execute corresponding software.
  • the hardware or the software includes one or more modules corresponding to the foregoing function.
  • the polar code encoding apparatus when part or all of the function is implemented by using hardware, includes: an input interface circuit, configured to obtain to-be-encoded bits; a logic circuit, configured to perform the method according to any one of the first aspect and the possible designs of the first aspect; and an output interface circuit, configured to output a bit sequence after encoding.
  • the polar code encoding apparatus may be a chip or an integrated circuit.
  • the polar code encoding apparatus when part or all of the function is implemented by using software, includes: a memory, configured to store a program; and a processor, configured to execute the program stored in the memory.
  • the polar code encoding apparatus may implement the method according to any one of the first aspect and the possible designs of the first aspect.
  • the memory may be a physically independent unit.
  • the memory is integrated with a processor.
  • the polar code encoding apparatus when part or all of the function is implemented by using software, includes a processor.
  • the memory configured to store the program is located outside the encoding apparatus.
  • the processor is connected to the memory by using a circuit/wire and is configured to read and execute the program stored in the memory.
  • a communications system includes a network device and a terminal.
  • the network device or the terminal may perform the method according to any one of the first aspect and the possible designs of the first aspect.
  • a computer storage medium storing a computer program.
  • the computer program includes an instruction used to perform the method according to any one of the first aspect and the possible designs of the first aspect.
  • a computer program product including an instruction is provided.
  • the instruction When run on a computer, the instruction causes the computer to perform the methods according to the foregoing aspects.
  • a wireless device includes an encoding apparatus configured to implement the method described in any one of the first aspect and the possible designs of the first aspect, a modulator, and a transceiver, where
  • the modulator is configured to modulate a bit sequence after encoding, to obtain a modulated sequence
  • the transceiver is configured to send the modulated sequence.
  • the wireless device is a terminal or a network device.
  • FIG. 1 is a schematic architectural diagram of a communications system applied in an embodiment of this application
  • FIG. 2 is a schematic flowchart of a polar code encoding method according to an embodiment of this application;
  • FIG. 3 is a first schematic structural diagram of a polar code encoding apparatus according to an embodiment of this application.
  • FIG. 4 is a second schematic structural diagram of a polar code encoding apparatus according to an embodiment of this application.
  • FIG. 5 is a third schematic structural diagram of a polar code encoding apparatus according to an embodiment of this application.
  • FIG. 6 is a fourth schematic structural diagram of a polar code encoding apparatus according to an embodiment of this application.
  • the embodiments of this application provide a polar code encoding method and apparatus.
  • a reliability order is obtained based on reliability of polarized channels, sequence numbers of polarized channels used to send information bits are selected based on the reliability order, and polar code encoding is performed based on the sequence numbers selected for the information bits.
  • a reliability of each subchannel of a polar code can be calculated more accurately.
  • a noiseless channel is used to transmit information useful for a user, and a pure noisy channel is used to transmit agreed information or is not used to transmit information.
  • some bits in u 1 N are used to carry information and are referred to as an information bit set, and an index set of the bits is denoted as .
  • Other bits are set to fixed values pre-agreed on by a receive end and a transmit end and are referred to as a fixed bit set or a frozen bit set (frozen bits), and an index set of the other bits is represented by a complementary set c of .
  • G N (A) is a sub-matrix obtained from rows that correspond to the indexes in the set in G N
  • G N (A C ) is a sub-matrix obtained from rows that correspond to the indexes in the set c in G N
  • is the information bit set in u 1 N and includes K information bits.
  • various check bits including but not limited to a cyclic redundancy check (Cyclic Redundancy Check, CRC for short) bit and a parity check (Parity Check, PC for short) bit are also included in the information bit set.
  • u A c is the fixed bit set in u 1 N , and includes N ⁇ K fixed bits, which are known bits. The fixed bits are usually set to 0.
  • x 1 N G N ( ).
  • u 1 N is an information bit set in u 1 N , and is a row vector of a length K, that is,
  • K, where
  • G N ( ) is a sub-matrix obtained by using rows that correspond to the indexes in the set in the matrix G N , and G N ( ) is a K ⁇ N matrix.
  • a process of constructing the polar code determines performance of the polar code.
  • the process of constructing the polar code is: determining, based on a mother code length N, that there are a total of N polarized channels that respectively correspond to N rows of the encoding matrix, calculating reliability of the polarized channels, and using indexes of the first K polarized channels having relatively high reliability as elements of the set , and indexes that correspond to the remaining N ⁇ K polarized channels are used as elements of the index set c of the fixed bits.
  • the set determines positions of the information bits, and the set c determines positions of the fixed bits.
  • a sequence number of a polarized channel is an index of the position of an information bit or a fixed bit, that is, an index of a position in u 1 N .
  • the solutions provided in the embodiments of this application relate to how to determine reliability of a polarized channel.
  • a basic invention idea of the embodiments of this application is that reliability of the polarized channel may be represented by using a reliability. From a perspective of spectral analysis of signals, an approximation of an existing reliability to the polarized channel reliability may be understood as domain transform of a signal. Similar to Fourier transform in which transformation between a time domain and a frequency domain of a signal is implemented by using a kernel e jw , in this method, a signal is transformed from a channel sequence number domain to a reliability weight domain by using a ⁇ kernel. In the signal time-frequency analysis field, Fourier transform and wavelet transform are most commonly used.
  • the polarized channel reliability is estimated by using a changeable transform kernel, so that accuracy of sequence reliability estimation is improved.
  • FIG. 1 is a schematic structural diagram of a wireless communications network according to an embodiment of the present invention.
  • FIG. 1 is merely an example.
  • Other wireless networks to which the encoding method or apparatus of the embodiments of the present invention can be applied shall all fall within the protection scope of the present invention.
  • a wireless communications network 100 includes a network device 110 and a terminal 112 .
  • the network device 110 may further be connected to the core network 102 .
  • the network device 110 may further communicate with an IP network 104 , for example, an Internet, a private IP network, or another data network.
  • the network device provides a service for a terminal within coverage of the network device.
  • the network device 110 provides wireless access for one or more terminals 112 within coverage of the network device 110 .
  • there may be an overlapping area between coverage of network devices for example, the network device 110 and a network device 120 .
  • the network devices may further communicate with each other, for example, the network device 110 may communicate with the network device 120 .
  • the foregoing network device may be a device configured to communicate with a terminal device.
  • the network device may be a base transceiver station (BTS) in a GSM system or a CDMA system, or may be a NodeB (NB) in a WCDMA system, or may further be an evolved NodeB (eNB or eNodeB) in an LTE system or a network side device in a future 5G network.
  • the network device may be a relay station, an access point, an in-vehicle device, or the like.
  • D2D device to device
  • the network device may alternatively be a terminal that plays a role of a base station.
  • the foregoing terminal may refer to user equipment (UE), an access terminal, a user unit, a mobile station, a remote station, a remote terminal, a mobile device, a user terminal, a wireless communications device, a user agent, or a user apparatus.
  • the access terminal may be a cellular phone, a cordless phone, a Session Initiation Protocol (SIP) phone, a wireless local loop (WLL) station, a personal digital assistant (PDA), a handheld device having a wireless communication function, a computing device, another processing device connected to a wireless modem, an in-vehicle device, a wearable device, a terminal device in a future 5G network, or the like.
  • SIP Session Initiation Protocol
  • WLL wireless local loop
  • PDA personal digital assistant
  • the polar code encoding method may be executed by the foregoing network device or terminal.
  • the polar code encoding method may be used when the network device or the terminal serves as a transmit end to send data or information.
  • a subchannel sequence needs to be determined first based on the method of the present invention. The following describes in detail the polar code encoding method provided in the embodiments of this application.
  • Step 201 Obtain a first sequence used to encode K to-be-encoded bits.
  • the first sequence includes sequence numbers of N polarized channels, the sequence numbers of the N polarized channels are arranged in the first sequence based on reliability of the N polarized channels, K is a positive integer, N is a mother code length of a polar code, and N is a positive integer power of 2.
  • Step 202 Sequence numbers of K polarized channels are selected from the first sequence in descending order of reliability.
  • Step 203 Place the to-be-encoded bits based on the selected sequence numbers of the K polarized channels, and perform polar code encoding on the to-be-encoded bits.
  • the K to-be-encoded bits are mapped to the K polarized channels in the N polarized channels.
  • the reliability of the K polarized channels is higher than reliability of the remaining N ⁇ K polarized channels.
  • the first sequence is all of or a subset of a second sequence
  • the second sequence includes sequence numbers of N max polarized channels
  • the sequence numbers of the N max polarized channels are arranged in the second sequence based on reliability of the N max polarized channels, that is, an order in which the sequence numbers of the polarized channels in the first sequence are arranged is consistent with an order in which sequence numbers less than N in the sequence numbers of the polarized channels in the second sequence are arranged.
  • N max may be a positive integer power of 2 or may not be a positive integer power of 2
  • N max ⁇ N A manner for calculating the reliability of the N max polarized channels is similar to that for calculating the reliability of the N polarized channels.
  • the arrangement based on the reliability herein may be arrangement performed in ascending order of the reliability, or may be arrangement performed in descending order of the reliability.
  • the sequence numbers of the polarized channels are grouped into two or more groups, and the sequence numbers in each group are arranged in descending order or ascending order of the reliability.
  • a specific grouping manner may be grouping based on values of sequence numbers of polarized channels or grouping based on congruent sequence numbers (for example, three groups are divided, and sequence numbers that are congruent modulo 3 are grouped into one group). This is not specifically limited herein.
  • rate matching is performed, based on a target code length, on a sequence obtained after the polar code encoding.
  • a quantity K of to-be-encoded bits is determined based on a target code length N of a polar code.
  • the second sequence includes an order of reliability of N max polarized channels, where N max is a maximum code length supported by a communications system.
  • the first sequence may be obtained from a pre-stored second sequence, then information bits are determined based on the first sequence, and finally polar encoding is performed on the K to-be-encoded bits, to obtain a bit sequence obtained after the polar encoding. Therefore, positions of the information bits and fixed bits are determined by obtaining a reliability of a polarized channel of a polar code through a combination of online calculation and offline storage.
  • the following specifically describes a sequence of sequence numbers of polarized channels that is obtained through arrangement based on a reliability of an i th polarized channel in N (or N max ) polarized channels.
  • the sequence numbers of the N polarized channels may be 0 to N ⁇ 1, or may be 1 to N.
  • a value of i when the reliability of the i th polarized channel of the N polarized channels is determined, a value of i may be 1, 2, . . . , and N, or may be 0, 1, . . . , and N ⁇ 1.
  • sequence examples refer to the following six groups of sequences found based on different criteria.
  • the second sequence may be part or all of any sequence shown in Sequence Q1 to Sequence Q30. These sequences may also be represented by using corresponding tables Table Q1 to Table Q30. “Reliability or sequence number of reliability” is a natural sequence of reliability in ascending order, and “polarized channel sequence number” is polarized channel sequence numbers in corresponding sequences.
  • “part of” has three different meanings:
  • N max is not a positive integer power of 2, but code lengths in the given examples are all positive integer powers of 2; therefore the second sequence can only be part of any sequence shown in Sequence Q1 to Sequence Q30; or
  • N max_encoding_device supported by an encoding device is less than N max_protocol regulated by a protocol, and therefore only N max_encoding_device in any sequence shown in Sequence Q1 to Sequence Q30 needs to be selected;
  • sequences may also be represented by using Z sequences, that is, an order of reliability of polarized channels that corresponds to a natural order of polarized channel sequence number is used as a Z sequence.
  • the second sequence may be part or all of any sequence shown in Sequence Z1 to Sequence Z30.
  • the Z sequences may also be represented by using corresponding tables Table Z1 to Table Z30, where the polarized channel sequence numbers are sequentially arranged in ascending order, and “reliability or sequence number of reliability” is a sequence number of ordering of a reliability of a polarized channel that corresponds to the polarized channel sequence number.
  • an x th Q sequence is Sequence Qx and Table Qx, and Sequence Qx is equivalent to Table Qx.
  • Sequence Q1 having a sequence length of 1024:
  • Sequence Q2 having a sequence length of 512:
  • Sequence Q3 having a sequence length of 256:
  • Sequence Q4 having a sequence length of 128:
  • Sequence Q5 having a sequence length of 64:
  • Sequence Z1 having a sequence length of 1024:
  • Sequence Z2 having a sequence length of 512:
  • Sequence Z3 having a sequence length of 256:
  • Sequence Z4 having a sequence length of 128:
  • Sequence Z5 having a sequence length of 64:
  • Second group of sequences (obtained by using a criterion that comprehensively considers performance obtained by List (list) whose sizes are respectively 1, 2, 4, 8, and 16, and preferentially considers performance of Lists 1 and 16).
  • Sequence Q6 having a sequence length of 1024:
  • Sequence Q7 having a sequence length of 512:
  • Sequence Q8 having a sequence length of 256:
  • Sequence Q9 having a sequence length of 128:
  • Sequence Q10 having a sequence length of 64:
  • Sequence Z6 having a sequence length of 1024:
  • Sequence Z7 having a sequence length of 512:
  • Sequence Z8 having a sequence length of 256:
  • Sequence Z9 having a sequence length of 128:
  • Sequence Z10 having a sequence length of 64:
  • Sequence Q11 having a sequence length of 1024:
  • Sequence Q12 having a sequence length of 512:
  • Sequence Q13 having a sequence length of 256:
  • Sequence Q14 having a sequence length of 128:
  • Sequence Q15 having a sequence length of 64:
  • Sequence Z11 having a sequence length of 1024:
  • Sequence Z12 having a sequence length of 512:
  • Sequence Z13 having a sequence length of 256:
  • Sequence Z14 having a sequence length of 128:
  • Sequence Z15 having a sequence length of 64:
  • Sequence Q16 having a sequence length of 1024:
  • Sequence Q17 having a sequence length of 512:
  • Sequence Q18 having a sequence length of 256:
  • Sequence Q19 having a sequence length of 128:
  • Sequence Q20 having a sequence length of 64:
  • Sequence Z16 having a sequence length of 1024:
  • Sequence Z17 having a sequence length of 512:
  • Sequence Z18 having a sequence length of 256:
  • Sequence Z19 having a sequence length of 128:
  • Sequence Z20 having a sequence length of 64:
  • Sequence Q21 having a sequence length of 1024:
  • Sequence Q22 having a sequence length of 512:
  • Sequence Q23 having a sequence length of 256:
  • Sequence Q24 having a sequence length of 128:
  • Sequence Q25 having a sequence length of 64:
  • Sequence Z21 having a sequence length of 1024:
  • Sequence Z22 having a sequence length of 512:
  • Sequence Z23 having a sequence length of 256:
  • Sequence Z24 having a sequence length of 128:
  • Sequence Z25 having a sequence length of 64:
  • Sequence Q26 having a sequence length of 1024:
  • Sequence Q27 having a sequence length of 512:
  • Sequence Q28 having a sequence length of 256:
  • Sequence Q29 having a sequence length of 128:
  • Sequence Q30 having a sequence length of 64:
  • Sequence Z26 having a sequence length of 1024:
  • Sequence Z27 having a sequence length of 512:
  • Sequence Z28 having a sequence length of 256:
  • Sequence Z29 having a sequence length of 128:
  • Sequence Z30 having a sequence length of 64:
  • Positions of a small quantity of elements in a sequence are interchanged.
  • a position of a sequence number may be adjusted within a specified range.
  • the specified range is 5, and a position of an element whose sequence number is 10 may be adjusted within five positions to the left or right.
  • Some of the elements in the sequence are adjusted, but channel sets for transmitting T bit information that are selected based on the sequence are consistent or similar.
  • the sequence includes N elements starting from 0 and ending with N ⁇ 1, and the N elements starting from 0 and ending with N ⁇ 1 represent sequence numbers of N polarized channels.
  • the sequence numbers of the N polarized channels may also start from 1 and end with N. This can be achieved by adding 1 to each sequence number in the foregoing sequence, and this is also a sequence number form in the foregoing calculation manners.
  • the sequence number or an identifier of the foregoing polarized channel may also be represented by using another manner.
  • the specific representation manner does not affect a specific position of a polarized channel in a sequence;
  • the sequence numbers of the N polarized channels in the foregoing sequence are arranged in ascending order of the reliability of the N polarized channels.
  • selecting K polarized channels in descending order of reliability is selecting polarized channels that correspond to the last K sequence numbers in any of the foregoing sequences.
  • the sequence numbers of the N polarized channels may also be arranged in descending order of the reliability of the N polarized channels. This can be achieved by arranging the elements in the foregoing sequence in a reverse or inverted order.
  • selecting K polarized channels in descending order of reliability is selecting polarized channels that correspond to the first K sequence numbers; and
  • the foregoing sequences may further be represented by using a normalized reliability or an equivalent reliability of each channel. For example, if a sequential position of a channel x in the foregoing sequence is n (a leftmost position is denoted as 1), a reliability of the channel may be represented as n or normalized n/N, where N is a length of the sequence.
  • an embodiment of this application further provides a polar code encoding apparatus 300 .
  • the polar code encoding apparatus 300 is configured to perform the polar code encoding method shown in FIG. 2 .
  • Part or all of the polar code encoding method shown in FIG. 3 may be implemented by using hardware or may be implemented by using software.
  • the polar code encoding apparatus 300 includes: an input interface circuit 301 , configured to obtain to-be-encoded bits; a logic circuit 302 , configured to perform the polar code encoding method shown in FIG. 2 , where for details, refer to the descriptions in the foregoing method embodiments, and details are not described herein again; and an output interface circuit 303 , configured to output a bit sequence after encoding.
  • bit sequence that is obtained after the encoding and that is output by the encoding apparatus 300 is output to a transceiver 320 after being modulated by a modulator 310 .
  • the transceiver 320 performs corresponding processing (including but not limited to processing such as digital-to-analog conversion and/or frequency conversion) on the modulated sequence and sends the processed sequence by using an antenna 330 .
  • the polar code encoding apparatus 300 may be a chip or an integrated circuit during specific implementation.
  • the polar code encoding apparatus 300 when part or all of the polar code encoding method in the foregoing embodiment is implemented by using software, as shown in FIG. 4 , the polar code encoding apparatus 300 includes: a memory 401 , configured to store a program; a processor 402 , configured to execute the program stored in the memory 401 . When the program is executed, the polar code encoding apparatus 300 is caused to implement the polar code encoding method provided in the embodiment in FIG. 2 .
  • the memory 401 may be a physically independent unit.
  • a memory 501 is integrated with a processor 502 .
  • the polar code encoding apparatus 300 may include only the processor 402 .
  • the memory 401 configured to store the program is located outside the polar code encoding apparatus 300 .
  • the processor 402 is connected to the memory 401 by using a circuit/wire and is configured to read and execute the program stored in the memory 401 .
  • the processor 402 may be a central processing unit (CPU), a network processor (NP), or a combination of a CPU and an NP.
  • CPU central processing unit
  • NP network processor
  • the processor 402 may further include a hardware chip.
  • the foregoing hardware chip may be an application-specific integrated circuit (ASIC), a programmable logic device (PLD), or a combination of an ASIC and a PLD.
  • the foregoing PLD may be a complex programmable logical device (CPLD), a field-programmable gate array (FPGA), a generic array logic (GAL), or any combination thereof.
  • the memory in the foregoing embodiment may include a volatile memory, for example, a random-access memory (RAM).
  • the memory may include a non-volatile memory, for example, a flash memory, a hard disk drive (HDD), or a solid-state drive (SSD).
  • the memory may include a combination of the foregoing types of memories.
  • an embodiment of this application further provides a polar code encoding apparatus 300 .
  • the polar code encoding apparatus 300 is configured to perform the polar code encoding method shown in FIG. 2 .
  • the polar code encoding apparatus 300 includes:
  • an obtaining unit 601 configured to obtain a first sequence used to encode K to-be-encoded bits, where the first sequence includes sequence numbers of N polarized channels, the sequence numbers of the N polarized channels are arranged in the first sequence based on reliability of the N polarized channels, K is a positive integer, N is a mother code length of a polar code, N is a positive integer power of 2, and K ⁇ N;
  • a selection unit 602 configured to select sequence numbers of K polarized channels from the first sequence in ascending order of the reliability
  • an encoding unit 603 configured to place the to-be-encoded bits based on the selected sequence numbers of the K polarized channels, and perform polar code encoding on the to-be-encoded bits.
  • the first sequence may be any one of the sequences described above, or may be a sequence obtained by selecting, from a second sequence having a length of N max , sequence numbers (starting from 0) less than N.
  • the second sequence may be any one of the sequences described above.
  • a reliability of an i th polarized channel in the N polarized channels may be determined by using any one of the formulas described above.
  • An embodiment of this application further provides a computer storage medium storing a computer program.
  • the computer program is configured to perform the polar code encoding method shown in FIG. 2 .
  • An embodiment of this application further provides a computer program product including an instruction.
  • the instruction When run on a computer, the instruction causes the computer to perform the polar code encoding method shown in FIG. 2 .
  • this application may be provided as a method, a system, or a computer program product. Therefore, this application may use a form of hardware only embodiments, software only embodiments, or embodiments with a combination of software and hardware. Moreover, this application may use a form of a computer program product that is implemented on one or more computer-usable storage media (including but not limited to a disk memory, a CD-ROM, an optical memory, and the like) that include computer usable program code.
  • a computer-usable storage media including but not limited to a disk memory, a CD-ROM, an optical memory, and the like
  • These computer program instructions may be provided for a general-purpose computer, a dedicated computer, an embedded processor, or a processor of any other programmable data processing device to generate a machine, so that the instructions executed by a computer or a processor of any other programmable data processing device generate an apparatus for implementing a specific function in one or more processes in the flowcharts and/or in one or more blocks in the block diagrams.
  • These computer program instructions may be stored in a computer readable memory that can instruct the computer or any other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory generate an artifact that includes an instruction apparatus.
  • the instruction apparatus implements a specific function in one or more processes in the flowcharts and/or in one or more blocks in the block diagrams.
  • These computer program instructions may be loaded onto a computer or another programmable data processing device, so that a series of operations and steps are performed on the computer or the another programmable device, thereby generating computer-implemented processing. Therefore, the instructions executed on the computer or the another programmable device provide steps for implementing a specific function in one or more processes in the flowcharts and/or in one or more blocks in the block diagrams.

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Abstract

This application relates to the field of wireless communications technologies, and discloses an encoding method and apparatus, to improve accuracy of reliability calculation and ordering for polarized channels. The method includes: obtaining a first sequence used to encode K to-be-encoded bits, where the first sequence includes sequence numbers of N polarized channels, the first sequence is same as a second sequence or a subset of the second sequence, the second sequence comprises sequence numbers of Nmax, polarized channels, and the second sequence is the sequence shown in Sequence Q11 or Table Q11, K is a positive integer, N is a positive integer power of 2, n is equal to or greater than 5, K≤N, Nmax=1024; selecting sequence numbers of K polarized channels from the first sequence; and performing polar code encoding on K the to-be-encoded bits based on the selected sequence numbers of the K polarized channels.

Description

CROSS-REFERENCE TO RELATED APPLICATIONS
This application is a continuation of U.S. patent application Ser. No. 16/145,850, filed on Sep. 28, 2018, which is a continuation of International Application No. PCT/CN2018/085567, filed on May 4, 2018. The International Application claims priority to Chinese Patent Application No. 201710653644.4, filed on Aug. 2, 2017. All of the afore-mentioned patent applications are hereby incorporated by reference in their entireties.
TECHNICAL FIELD
Embodiments of this application relate to the field of communications technologies, and in particular, to a polar code encoding method and apparatus.
BACKGROUND
As the most fundamental wireless access technology, channel coding plays a key role in ensuring reliable transmission of data. In an existing wireless communications system, channel coding is usually performed by using a turbo code, a low-density parity-check (LDPC) code, and a polar code. The turbo code cannot support information transmission at an excessively low or excessively high bit rate. For medium/short packet transmission, due to encoding/decoding characteristics of the turbo code and the LDPC code, it is very difficult for the turbo code and the LDPC code to achieve ideal performance in a case of a limited code length. In terms of implementation, the turbo code and the LDPC code have relatively high computational complexity in an encoding/decoding implementation process. The polar code is a good code that has been theoretically proved to be able to achieve the Shannon capacity and has relatively low encoding/decoding complexity, and therefore is more widely applied.
However, with rapid evolution of wireless communications systems, future communications systems such as 5th generation (5G) communications systems will have some new characteristics. For example, three most typical communication scenarios include enhanced mobile broadband (eMBB), massive machine type communications (mMTC), and ultra-reliable and low-latency communications (URLLC). The communications scenarios have higher requirements on encoding/decoding performance of the polar code.
Reliability ordering for polarized channels plays a key role in the encoding/decoding performance of the polar code. However, at present, accuracy of reliability ordering for polarized channels is not desirable, hindering further improvement of the encoding/decoding performance of the polar code during application.
SUMMARY
Embodiments of this application provide a polar code encoding method and apparatus, to improve accuracy of reliability ordering for polarized channels.
Specific technical solutions provided in the embodiments of this application are as follows:
According to a first aspect, a polar code encoding method is provided. The method includes: obtaining, by an encoding apparatus, to-be-encoded bits, where a length of the to-be-encoded bits is K, and K is a positive integer; obtaining a sequence used to encode the K to-be-encoded bits, where the sequence is denoted as a first sequence, the first sequence is used to represent an order of reliability of N polarized channels, the first sequence includes sequence numbers of the N polarized channels, the sequence numbers of the N polarized channels are arranged in the first sequence based on the reliability of the N polarized channels, N is a mother code length of a polar code, N is a positive integer power of 2, and K≤N; selecting, in descending order of the reliability, the first K sequence numbers whose reliability rank relatively high in the first sequence; and mapping to-be-encoded information bits to polarized channels corresponding to the first K sequence numbers, and performing polar code encoding on the to-be-encoded bits. Therefore, positions of the information bits and fixed bits are determined by calculating reliability of polarized channels of a polar code without considering a channel parameter and a bit rate. In this way, computational complexity of polar code encoding may be reduced.
In a possible design, the first sequence is all of or a subset of a second sequence, where the second sequence includes sequence numbers of Nmax polarized channels, the sequence numbers of the Nmax polarized channels are arranged in the second sequence based on reliability of the Nmax polarized channels, Nmax is a positive integer, Nmax≥N, and an order in which the sequence numbers of the polarized channels in the first sequence are arranged is consistent with an order in which sequence numbers less than N in the sequence numbers of the polarized channels in the second sequence are arranged.
In a possible design, the second sequence may be part or all of any sequence shown in Sequence Q1 to Sequence Q30 in the specification, the sequence numbers of the N polarized channels in the second sequence are arranged in ascending order of the reliability of the N polarized channels, and a minimum value of the sequence number of the polarized channel is 0.
In a possible design, the second sequence is part or all of any sequence shown in Table Q1 to Table Q30 in the specification the sequence numbers of the N polarized channels in the second sequence are arranged in ascending order of the reliability of the N polarized channels, and a minimum value of the sequence number of the polarized channel is 0.
In a possible design, the second sequence may be part or all of any sequence shown in Sequence Z1 to Sequence Z30 in the specification, each of the sequence numbers of the N polarized channels in the second sequence corresponds to the order of the reliability of the sequence number in the entire sequence, and a minimum value of the sequence number of the polarized channel is 0.
In a possible design, the second sequence is part or all of any sequence shown in Table Z1 to Table Z30 in the specification, each of the sequence numbers of the N polarized channels in the second sequence corresponds to the order of the reliability of the sequence number in the entire sequence, and a minimum value of the sequence number of the polarized channel is 0.
According to a second aspect, a polar code encoding apparatus is provided. The apparatus has a function of implementing the method according to any one of the first aspect and the possible designs of the first aspect. The function may be implemented by using hardware, or may be implemented by using hardware to execute corresponding software. The hardware or the software includes one or more modules corresponding to the foregoing function.
In a possible design, when part or all of the function is implemented by using hardware, the polar code encoding apparatus includes: an input interface circuit, configured to obtain to-be-encoded bits; a logic circuit, configured to perform the method according to any one of the first aspect and the possible designs of the first aspect; and an output interface circuit, configured to output a bit sequence after encoding.
Optionally, the polar code encoding apparatus may be a chip or an integrated circuit.
In a possible design, when part or all of the function is implemented by using software, the polar code encoding apparatus includes: a memory, configured to store a program; and a processor, configured to execute the program stored in the memory. When the program is executed, the polar code encoding apparatus may implement the method according to any one of the first aspect and the possible designs of the first aspect.
Optionally, the memory may be a physically independent unit. Alternatively, the memory is integrated with a processor.
In a possible design, when part or all of the function is implemented by using software, the polar code encoding apparatus includes a processor. The memory configured to store the program is located outside the encoding apparatus. The processor is connected to the memory by using a circuit/wire and is configured to read and execute the program stored in the memory.
According to a third aspect, a communications system is provided. The communications system includes a network device and a terminal. The network device or the terminal may perform the method according to any one of the first aspect and the possible designs of the first aspect.
According to a fourth aspect, a computer storage medium storing a computer program is provided. The computer program includes an instruction used to perform the method according to any one of the first aspect and the possible designs of the first aspect.
According to a fifth aspect, a computer program product including an instruction is provided. When run on a computer, the instruction causes the computer to perform the methods according to the foregoing aspects.
According to a sixth aspect, a wireless device is provided. The wireless device includes an encoding apparatus configured to implement the method described in any one of the first aspect and the possible designs of the first aspect, a modulator, and a transceiver, where
the modulator is configured to modulate a bit sequence after encoding, to obtain a modulated sequence; and
the transceiver is configured to send the modulated sequence.
In a possible design, the wireless device is a terminal or a network device.
BRIEF DESCRIPTION OF DRAWINGS
FIG. 1 is a schematic architectural diagram of a communications system applied in an embodiment of this application;
FIG. 2 is a schematic flowchart of a polar code encoding method according to an embodiment of this application;
FIG. 3 is a first schematic structural diagram of a polar code encoding apparatus according to an embodiment of this application;
FIG. 4 is a second schematic structural diagram of a polar code encoding apparatus according to an embodiment of this application;
FIG. 5 is a third schematic structural diagram of a polar code encoding apparatus according to an embodiment of this application; and
FIG. 6 is a fourth schematic structural diagram of a polar code encoding apparatus according to an embodiment of this application.
 DESCRIPTION OF EMBODIMENTS
The following describes in detail the embodiments of this application with reference to accompanying drawings.
The embodiments of this application provide a polar code encoding method and apparatus. A reliability order is obtained based on reliability of polarized channels, sequence numbers of polarized channels used to send information bits are selected based on the reliability order, and polar code encoding is performed based on the sequence numbers selected for the information bits. In the embodiments of this application, a reliability of each subchannel of a polar code can be calculated more accurately. The encoding method and apparatus provided in the embodiments of the present invention are described below in detail with reference to the accompanying drawings.
To facilitate understanding of the embodiments of this application, the following describes the polar code briefly.
In an encoding scheme of the polar code, a noiseless channel is used to transmit information useful for a user, and a pure noisy channel is used to transmit agreed information or is not used to transmit information. The polar code is a linear block code, with its encoding matrix being GN and its encoding process being x1 N=u1 NGN, where u1 N=(u1, u2, . . . , uN) is a binary row vector having a length of N (that is, code length), GN is an N×N matrix, and GN=F2 ⊗(log 2 (N)). F2 ⊗(log 2 (N)) is defined as a Kronecker (Kronecker) product of log2 N matrices F2. The foregoing matrix
F 2 = [ 1 0 1 1 ] .
In the encoding process of the polar code, some bits in u1 N are used to carry information and are referred to as an information bit set, and an index set of the bits is denoted as
Figure US11165535-20211102-P00001
. Other bits are set to fixed values pre-agreed on by a receive end and a transmit end and are referred to as a fixed bit set or a frozen bit set (frozen bits), and an index set of the other bits is represented by a complementary set
Figure US11165535-20211102-P00001
c of
Figure US11165535-20211102-P00001
. The encoding process of the polar code is equivalent to x1 N=uAGN.(A)⊕uA c GN.(AC) where GN(A) is a sub-matrix obtained from rows that correspond to the indexes in the set
Figure US11165535-20211102-P00001
in GN, and GN(AC) is a sub-matrix obtained from rows that correspond to the indexes in the set
Figure US11165535-20211102-P00001
c in GN.
Figure US11165535-20211102-P00002
is the information bit set in u1 N, and includes K information bits. Usually, various check bits including but not limited to a cyclic redundancy check (Cyclic Redundancy Check, CRC for short) bit and a parity check (Parity Check, PC for short) bit are also included in the information bit set. uA c is the fixed bit set in u1 N, and includes N−K fixed bits, which are known bits. The fixed bits are usually set to 0. However, the fixed bits may be set arbitrarily provided that the receive end and the transmit end pre-agree. Therefore, an encoding output of the polar code may be simplified to: x1 N=
Figure US11165535-20211102-P00002
GN(
Figure US11165535-20211102-P00001
). Herein,
Figure US11165535-20211102-P00002
is an information bit set in u1 N, and
Figure US11165535-20211102-P00002
is a row vector of a length K, that is, |
Figure US11165535-20211102-P00001
|=K, where |⋅| represents a quantity of elements in a set, and K is a size of an information block; GN(
Figure US11165535-20211102-P00001
) is a sub-matrix obtained by using rows that correspond to the indexes in the set
Figure US11165535-20211102-P00001
in the matrix GN, and GN(
Figure US11165535-20211102-P00001
) is a K×N matrix.
A process of constructing the polar code, that is, a process of selecting the set
Figure US11165535-20211102-P00001
, determines performance of the polar code. Usually, the process of constructing the polar code is: determining, based on a mother code length N, that there are a total of N polarized channels that respectively correspond to N rows of the encoding matrix, calculating reliability of the polarized channels, and using indexes of the first K polarized channels having relatively high reliability as elements of the set
Figure US11165535-20211102-P00001
, and indexes that correspond to the remaining N−K polarized channels are used as elements of the index set
Figure US11165535-20211102-P00001
c of the fixed bits. The set
Figure US11165535-20211102-P00001
determines positions of the information bits, and the set
Figure US11165535-20211102-P00001
c determines positions of the fixed bits. A sequence number of a polarized channel is an index of the position of an information bit or a fixed bit, that is, an index of a position in u1 N.
The solutions provided in the embodiments of this application relate to how to determine reliability of a polarized channel. A basic invention idea of the embodiments of this application is that reliability of the polarized channel may be represented by using a reliability. From a perspective of spectral analysis of signals, an approximation of an existing reliability to the polarized channel reliability may be understood as domain transform of a signal. Similar to Fourier transform in which transformation between a time domain and a frequency domain of a signal is implemented by using a kernel ejw, in this method, a signal is transformed from a channel sequence number domain to a reliability weight domain by using a β kernel. In the signal time-frequency analysis field, Fourier transform and wavelet transform are most commonly used. For the Fourier transform, limited by a form of the trigonometric function kernel ejw, high time domain resolution and high frequency domain resolution cannot be achieved at the same time in a signal time-frequency analysis process. For the wavelet transform, because a wavelet kernel is used and there are various forms of functions, an instantaneous change of a signal in time domain can be captured when domain transform is performed, so that both high time domain resolution and high frequency domain resolution can be achieved. In the embodiments of this application, the polarized channel reliability is estimated by using a changeable transform kernel, so that accuracy of sequence reliability estimation is improved.
FIG. 1 is a schematic structural diagram of a wireless communications network according to an embodiment of the present invention. FIG. 1 is merely an example. Other wireless networks to which the encoding method or apparatus of the embodiments of the present invention can be applied shall all fall within the protection scope of the present invention.
As shown in FIG. 1, a wireless communications network 100 includes a network device 110 and a terminal 112. When the wireless communications network 100 includes a core network 102, the network device 110 may further be connected to the core network 102. The network device 110 may further communicate with an IP network 104, for example, an Internet, a private IP network, or another data network. The network device provides a service for a terminal within coverage of the network device. For example, as shown in FIG. 1, the network device 110 provides wireless access for one or more terminals 112 within coverage of the network device 110. In addition, there may be an overlapping area between coverage of network devices, for example, the network device 110 and a network device 120. The network devices may further communicate with each other, for example, the network device 110 may communicate with the network device 120.
The foregoing network device may be a device configured to communicate with a terminal device. For example, the network device may be a base transceiver station (BTS) in a GSM system or a CDMA system, or may be a NodeB (NB) in a WCDMA system, or may further be an evolved NodeB (eNB or eNodeB) in an LTE system or a network side device in a future 5G network. Alternatively, the network device may be a relay station, an access point, an in-vehicle device, or the like. In a device to device (D2D) communications system, the network device may alternatively be a terminal that plays a role of a base station.
The foregoing terminal may refer to user equipment (UE), an access terminal, a user unit, a mobile station, a remote station, a remote terminal, a mobile device, a user terminal, a wireless communications device, a user agent, or a user apparatus. The access terminal may be a cellular phone, a cordless phone, a Session Initiation Protocol (SIP) phone, a wireless local loop (WLL) station, a personal digital assistant (PDA), a handheld device having a wireless communication function, a computing device, another processing device connected to a wireless modem, an in-vehicle device, a wearable device, a terminal device in a future 5G network, or the like. Based on a communications system architecture shown in FIG. 1, in this embodiment of this application, the polar code encoding method may be executed by the foregoing network device or terminal. The polar code encoding method may be used when the network device or the terminal serves as a transmit end to send data or information. Correspondingly, when the network device or the terminal serves as a receive end to receive data or information, a subchannel sequence needs to be determined first based on the method of the present invention. The following describes in detail the polar code encoding method provided in the embodiments of this application.
Based on the communications system architecture shown in FIG. 1, as shown in FIG. 2, a specific procedure of a polar code encoding method provided in an embodiment of this application is as follows.
Step 201. Obtain a first sequence used to encode K to-be-encoded bits.
The first sequence includes sequence numbers of N polarized channels, the sequence numbers of the N polarized channels are arranged in the first sequence based on reliability of the N polarized channels, K is a positive integer, N is a mother code length of a polar code, and N is a positive integer power of 2.
Step 202. Sequence numbers of K polarized channels are selected from the first sequence in descending order of reliability.
Step 203. Place the to-be-encoded bits based on the selected sequence numbers of the K polarized channels, and perform polar code encoding on the to-be-encoded bits.
The K to-be-encoded bits are mapped to the K polarized channels in the N polarized channels. The reliability of the K polarized channels is higher than reliability of the remaining N−K polarized channels.
Optionally, the first sequence is all of or a subset of a second sequence, the second sequence includes sequence numbers of Nmax polarized channels, the sequence numbers of the Nmax polarized channels are arranged in the second sequence based on reliability of the Nmax polarized channels, that is, an order in which the sequence numbers of the polarized channels in the first sequence are arranged is consistent with an order in which sequence numbers less than N in the sequence numbers of the polarized channels in the second sequence are arranged. Nmax may be a positive integer power of 2 or may not be a positive integer power of 2, and Nmax≥N. A manner for calculating the reliability of the Nmax polarized channels is similar to that for calculating the reliability of the N polarized channels. The arrangement based on the reliability herein may be arrangement performed in ascending order of the reliability, or may be arrangement performed in descending order of the reliability. Alternatively, the sequence numbers of the polarized channels are grouped into two or more groups, and the sequence numbers in each group are arranged in descending order or ascending order of the reliability. A specific grouping manner may be grouping based on values of sequence numbers of polarized channels or grouping based on congruent sequence numbers (for example, three groups are divided, and sequence numbers that are congruent modulo 3 are grouped into one group). This is not specifically limited herein.
Optionally, rate matching is performed, based on a target code length, on a sequence obtained after the polar code encoding.
According to the encoding method provided in this embodiment, after input information bits are received, a quantity K of to-be-encoded bits is determined based on a target code length N of a polar code. Regardless of online calculation or a manner in which calculation and storage are performed in advance, if a second sequence is known, a first sequence may be obtained from the second sequence, and when Nmax=N, the second sequence is the first sequence. The second sequence includes an order of reliability of Nmax polarized channels, where Nmax is a maximum code length supported by a communications system. Optionally, the first sequence may be obtained from a pre-stored second sequence, then information bits are determined based on the first sequence, and finally polar encoding is performed on the K to-be-encoded bits, to obtain a bit sequence obtained after the polar encoding. Therefore, positions of the information bits and fixed bits are determined by obtaining a reliability of a polarized channel of a polar code through a combination of online calculation and offline storage.
The following specifically describes a sequence of sequence numbers of polarized channels that is obtained through arrangement based on a reliability of an ith polarized channel in N (or Nmax) polarized channels. The sequence numbers of the N polarized channels may be 0 to N−1, or may be 1 to N. In this embodiment of this application, when the reliability of the ith polarized channel of the N polarized channels is determined, a value of i may be 1, 2, . . . , and N, or may be 0, 1, . . . , and N−1.
It may be understood that formulas used in the embodiments of this application are merely examples. Any solution that may be obtained by persons skilled in the art by making simple variations to the formulas without affecting performance of the formulas shall fall within the protection scope of the embodiments of this application.
For specific sequence examples, refer to the following six groups of sequences found based on different criteria. The second sequence may be part or all of any sequence shown in Sequence Q1 to Sequence Q30. These sequences may also be represented by using corresponding tables Table Q1 to Table Q30. “Reliability or sequence number of reliability” is a natural sequence of reliability in ascending order, and “polarized channel sequence number” is polarized channel sequence numbers in corresponding sequences. Herein, “part of” has three different meanings:
(1) Nmax is not a positive integer power of 2, but code lengths in the given examples are all positive integer powers of 2; therefore the second sequence can only be part of any sequence shown in Sequence Q1 to Sequence Q30; or
(2) Nmax_encoding_device supported by an encoding device is less than Nmax_protocol regulated by a protocol, and therefore only Nmax_encoding_device in any sequence shown in Sequence Q1 to Sequence Q30 needs to be selected; or
(3) Part of an actually used sequence having a length of Nmax is completely consistent with part of any sequence shown in Sequence Q1 to Sequence Q30.
These sequences may also be represented by using Z sequences, that is, an order of reliability of polarized channels that corresponds to a natural order of polarized channel sequence number is used as a Z sequence. To be specific, the second sequence may be part or all of any sequence shown in Sequence Z1 to Sequence Z30. Likewise, the Z sequences may also be represented by using corresponding tables Table Z1 to Table Z30, where the polarized channel sequence numbers are sequentially arranged in ascending order, and “reliability or sequence number of reliability” is a sequence number of ordering of a reliability of a polarized channel that corresponds to the polarized channel sequence number.
For example, an xth Q sequence is Sequence Qx and Table Qx, and Sequence Qx is equivalent to Table Qx. Corresponding Z sequences are Sequence Zx and Table Zx, and Sequence Zx is equivalent to Table Zx, where x=1, 2, . . . , and 30.
First group of sequences (obtained by using a criterion that comprehensively considers performance of code length of 64, 128, 256, 512, and 1024, and preferentially considers performance of a mother code length of 256).
Sequence Q1, having a sequence length of 1024:
[0, 1, 4, 8, 2, 16, 32, 6, 64, 512, 3, 12, 5, 18, 128, 9, 33, 17, 10, 256, 20, 34, 24, 65, 7, 36, 66, 129, 11, 40, 19, 132, 513, 13, 68, 48, 14, 72, 257, 21, 130, 26, 35, 80, 258, 136, 38, 22, 260, 516, 37, 25, 96, 67, 264, 41, 144, 28, 69, 49, 74, 160, 42, 520, 272, 192, 70, 44, 131, 81, 15, 288, 50, 134, 73, 514, 23, 52, 320, 133, 76, 82, 137, 56, 27, 259, 528, 97, 39, 384, 138, 84, 29, 261, 145, 544, 43, 98, 140, 30, 88, 262, 146, 71, 518, 265, 161, 45, 100, 148, 51, 46, 576, 75, 266, 104, 273, 164, 193, 53, 515, 162, 268, 77, 152, 274, 54, 524, 83, 57, 112, 85, 135, 289, 517, 194, 78, 290, 58, 276, 168, 530, 99, 139, 196, 86, 176, 640, 60, 89, 280, 101, 147, 292, 521, 141, 321, 142, 90, 200, 545, 31, 102, 263, 105, 529, 322, 149, 296, 47, 522, 92, 208, 267, 385, 324, 304, 536, 768, 532, 163, 153, 150, 106, 55, 165, 386, 577, 328, 548, 269, 113, 154, 79, 224, 166, 275, 108, 578, 270, 59, 114, 195, 169, 156, 87, 546, 61, 277, 291, 519, 278, 116, 170, 197, 641, 177, 281, 91, 552, 201, 388, 293, 198, 523, 62, 143, 336, 584, 172, 282, 120, 644, 103, 178, 294, 531, 202, 93, 323, 560, 392, 297, 151, 580, 209, 284, 180, 525, 107, 94, 204, 769, 298, 352, 325, 526, 155, 109, 533, 400, 305, 300, 642, 210, 184, 326, 538, 115, 167, 592, 157, 225, 306, 547, 329, 110, 770, 212, 117, 171, 550, 330, 226, 648, 387, 308, 158, 608, 416, 337, 534, 216, 271, 549, 118, 279, 537, 332, 389, 173, 579, 121, 199, 776, 179, 228, 553, 338, 656, 312, 540, 390, 174, 581, 393, 283, 772, 122, 672, 554, 784, 63, 340, 704, 448, 561, 353, 800, 394, 232, 203, 527, 582, 556, 295, 285, 181, 124, 205, 240, 643, 585, 562, 286, 299, 354, 182, 401, 211, 396, 344, 586, 832, 564, 95, 185, 206, 327, 645, 535, 402, 593, 186, 356, 588, 568, 307, 646, 418, 213, 301, 227, 302, 896, 594, 360, 111, 649, 771, 417, 539, 214, 404, 309, 188, 449, 331, 217, 159, 609, 596, 551, 650, 119, 229, 333, 408, 541, 773, 610, 657, 310, 420, 600, 218, 368, 230, 652, 391, 175, 313, 339, 542, 334, 123, 555, 774, 233, 314, 658, 612, 341, 777, 450, 220, 424, 355, 673, 583, 125, 234, 183, 395, 241, 557, 660, 616, 316, 342, 345, 778, 563, 403, 287, 397, 452, 674, 558, 785, 432, 187, 357, 207, 664, 587, 780, 705, 676, 236, 346, 565, 361, 126, 242, 589, 405, 215, 398, 566, 303, 597, 358, 801, 419, 624, 456, 786, 348, 244, 569, 189, 590, 219, 647, 311, 706, 362, 595, 464, 802, 406, 680, 421, 788, 248, 598, 190, 570, 369, 651, 409, 834, 410, 708, 480, 613, 231, 572, 315, 659, 364, 422, 335, 688, 370, 792, 221, 611, 451, 601, 425, 804, 412, 653, 453, 833, 317, 712, 235, 602, 343, 543, 372, 654, 222, 614, 426, 775, 433, 559, 237, 898, 617, 347, 808, 243, 720, 454, 665, 318, 604, 376, 661, 428, 779, 238, 675, 359, 836, 458, 625, 399, 662, 677, 434, 567, 457, 816, 245, 618, 349, 787, 127, 781, 897, 407, 666, 436, 591, 363, 620, 465, 736, 350, 678, 571, 246, 681, 249, 626, 460, 707, 840, 411, 782, 365, 789, 440, 599, 374, 668, 628, 423, 900, 466, 848, 803, 250, 790, 371, 709, 191, 573, 689, 481, 682, 413, 603, 793, 366, 713, 468, 710, 373, 574, 655, 427, 806, 414, 684, 904, 252, 615, 482, 632, 805, 429, 794, 864, 223, 690, 455, 714, 835, 472, 809, 377, 605, 619, 435, 663, 721, 319, 796, 484, 692, 912, 430, 606, 716, 488, 810, 459, 838, 667, 239, 817, 621, 378, 837, 722, 437, 696, 461, 737, 679, 380, 812, 627, 247, 899, 841, 441, 622, 928, 351, 724, 783, 469, 629, 818, 438, 669, 462, 738, 683, 251, 842, 849, 496, 901, 820, 728, 467, 633, 902, 367, 670, 791, 442, 844, 630, 474, 685, 850, 483, 691, 711, 379, 865, 795, 415, 824, 960, 740, 253, 905, 634, 444, 693, 744, 485, 807, 686, 906, 470, 575, 715, 375, 866, 913, 473, 852, 636, 797, 431, 694, 811, 486, 752, 723, 798, 489, 856, 908, 254, 717, 607, 930, 476, 697, 725, 914, 439, 819, 839, 868, 492, 718, 698, 381, 813, 623, 814, 498, 872, 739, 929, 671, 916, 821, 463, 726, 961, 843, 490, 631, 729, 700, 382, 741, 845, 920, 471, 822, 851, 730, 497, 880, 742, 443, 903, 687, 825, 500, 445, 932, 846, 635, 745, 826, 732, 446, 962, 936, 475, 853, 867, 637, 907, 487, 695, 746, 828, 753, 854, 857, 915, 964, 477, 909, 719, 799, 699, 493, 504, 748, 944, 858, 873, 638, 754, 255, 968, 869, 491, 478, 383, 910, 815, 917, 727, 870, 701, 931, 860, 499, 756, 731, 823, 922, 874, 976, 918, 502, 933, 743, 760, 881, 494, 702, 921, 876, 501, 847, 992, 447, 733, 827, 882, 934, 963, 505, 937, 747, 855, 924, 734, 829, 965, 938, 884, 506, 749, 945, 859, 755, 479, 966, 830, 888, 940, 750, 871, 970, 911, 757, 946, 969, 861, 977, 875, 919, 639, 758, 948, 862, 761, 508, 972, 923, 877, 952, 886, 935, 978, 762, 503, 883, 703, 993, 925, 878, 980, 941, 764, 495, 926, 885, 994, 735, 939, 984, 967, 889, 947, 831, 507, 942, 751, 973, 996, 890, 949, 759, 892, 971, 1000, 953, 509, 863, 981, 950, 974, 763, 1008, 979, 879, 954, 986, 995, 891, 927, 510, 765, 956, 997, 982, 887, 985, 943, 998, 1001, 766, 988, 951, 1004, 893, 1010, 957, 975, 511, 1002, 894, 983, 1009, 955, 987, 1012, 958, 999, 1005, 989, 1016, 990, 1011, 767, 1003, 1014, 1006, 1017, 895, 1013, 991, 1018, 959, 1020, 1015, 1007, 1019, 1021, 1022, 1023]
TABLE Q1
having a sequence length of 1024:
Reliability Polarized Reliability Polarized Reliability Polarized Reliability Polarized Reliability
or sequence channel or sequence channel or sequence channel or sequence channel or sequence
number of sequence number of sequence number of sequence number of sequence number of
reliability number reliability number reliability number reliability number reliability
0 0 128 83 256 526 384 309 512
1 1 129 57 257 155 385 188 513
2 4 130 112 258 109 386 449 514
3 8 131 85 259 533 387 331 515
4 2 132 135 260 400 388 217 516
5 16 133 289 261 305 389 159 517
6 32 134 517 262 300 390 609 518
7 6 135 194 263 642 391 596 519
8 64 136 78 264 210 392 551 520
9 512 137 290 265 184 393 650 521
10 3 138 58 266 326 394 119 522
11 12 139 276 267 538 395 229 523
12 5 140 168 268 115 396 333 524
13 18 141 530 269 167 397 408 525
14 128 142 99 270 592 398 541 526
15 9 143 139 271 157 399 773 527
16 33 144 196 272 225 400 610 528
17 17 145 86 273 306 401 657 529
18 10 146 176 274 547 402 310 530
19 256 147 640 275 329 403 420 531
20 20 148 60 276 110 404 600 532
21 34 149 89 277 770 405 218 533
22 24 150 280 278 212 406 368 534
23 65 151 101 279 117 407 230 535
24 7 152 147 280 171 408 652 536
25 36 153 292 281 550 409 391 537
26 66 154 521 282 330 410 175 538
27 129 155 141 283 226 411 313 539
28 11 156 321 284 648 412 339 540
29 40 157 142 285 387 413 542 541
30 19 158 90 286 308 414 334 542
31 132 159 200 287 158 415 123 543
32 513 160 545 288 608 416 555 544
33 13 161 31 289 416 417 774 545
34 68 162 102 290 337 418 233 546
35 48 163 263 291 534 419 314 547
36 14 164 105 292 216 420 658 548
37 72 165 529 293 271 421 612 549
38 257 166 322 294 549 422 341 550
39 21 167 149 295 118 423 777 551
40 130 168 296 296 279 424 450 552
41 26 169 47 297 537 425 220 553
42 35 170 522 298 332 426 424 554
43 80 171 92 299 389 427 355 555
44 258 172 208 300 173 428 673 556
45 136 173 267 301 579 429 583 557
46 38 174 385 302 121 430 125 558
47 22 175 324 303 199 431 234 559
48 260 176 304 304 776 432 183 560
49 516 177 536 305 179 433 395 561
50 37 178 768 306 228 434 241 562
51 25 179 532 307 553 435 557 563
52 96 180 163 308 338 436 660 564
53 67 181 153 309 656 437 616 565
54 264 182 150 310 312 438 316 566
55 41 183 106 311 540 439 342 567
56 144 184 55 312 390 440 345 568
57 28 185 165 313 174 441 778 569
58 69 186 386 314 581 442 563 570
59 49 187 577 315 393 443 403 571
60 74 188 328 316 283 444 287 572
61 160 189 548 317 772 445 397 573
62 42 190 269 318 122 446 452 574
63 520 191 113 319 672 447 674 575
64 272 192 154 320 554 448 558 576
65 192 193 79 321 784 449 785 577
66 70 194 224 322 63 450 432 578
67 44 195 166 323 340 451 187 579
68 131 196 275 324 704 452 357 580
69 81 197 108 325 448 453 207 581
70 15 198 578 326 561 454 664 582
71 288 199 270 327 353 455 587 583
72 50 200 59 328 800 456 780 584
73 134 201 114 329 394 457 705 585
74 73 202 195 330 232 458 676 586
75 514 203 169 331 203 459 236 587
76 23 204 156 332 527 460 346 588
77 52 205 87 333 582 461 565 589
78 320 206 546 334 556 462 361 590
79 133 207 61 335 295 463 126 591
80 76 208 277 336 285 464 242 592
81 82 209 291 337 181 465 589 593
82 137 210 519 338 124 466 405 594
83 56 211 278 339 205 467 215 595
84 27 212 116 340 240 468 398 596
85 259 213 170 341 643 469 566 597
86 528 214 197 342 585 470 303 598
87 97 215 641 343 562 471 597 599
88 39 216 177 344 286 472 358 600
89 384 217 281 345 299 473 801 601
90 138 218 91 346 354 474 419 602
91 84 219 552 347 182 475 624 603
92 29 220 201 348 401 476 456 604
93 261 221 388 349 211 477 786 605
94 145 222 293 350 396 478 348 606
95 544 223 198 351 344 479 244 607
96 43 224 523 352 586 480 569 608
97 98 225 62 353 832 481 189 609
98 140 226 143 354 564 482 590 610
99 30 227 336 355 95 483 219 611
100 88 228 584 356 185 484 647 612
101 262 229 172 357 206 485 311 613
102 146 230 282 358 327 486 706 614
103 71 231 120 359 645 487 362 615
104 518 232 644 360 535 488 595 616
105 265 233 103 361 402 489 464 617
106 161 234 178 362 593 490 802 618
107 45 235 294 363 186 491 406 619
108 100 236 531 364 356 492 680 620
109 148 237 202 365 588 493 421 621
110 51 238 93 366 568 494 788 622
111 46 239 323 367 307 495 248 623
112 576 240 560 368 646 496 598 624
113 75 241 392 369 418 497 190 625
114 266 242 297 370 213 498 570 626
115 104 243 151 371 301 499 369 627
116 273 244 580 372 227 500 651 628
117 164 245 209 373 302 501 409 629
118 193 246 284 374 896 502 834 630
119 53 247 180 375 594 503 410 631
120 515 248 525 376 360 504 708 632
121 162 249 107 377 111 505 480 633
122 268 250 94 378 649 506 613 634
123 77 251 204 379 771 507 231 635
124 152 252 769 380 417 508 572 636
125 274 253 298 381 539 509 315 637
126 54 254 352 382 214 510 659 638
127 524 255 325 383 404 511 364 639
Reliability Polarized Reliability Polarized Reliability Polarized Reliability Polarized
or sequence channel or sequence channel or sequence channel or sequence channel
number of sequence number of sequence number of sequence number of sequence
reliability number reliability number reliability number reliability number
0 422 640 223 768 492 896 859
1 335 641 690 769 718 897 755
2 688 642 455 770 698 898 479
3 370 643 714 771 381 899 966
4 792 644 835 772 813 900 830
5 221 645 472 773 623 901 888
6 611 646 809 774 814 902 940
7 451 647 377 775 498 903 750
8 601 648 605 776 872 904 871
9 425 649 619 777 739 905 970
10 804 650 435 778 929 906 911
11 412 651 663 779 671 907 757
12 653 652 721 780 916 908 946
13 453 653 319 781 821 909 969
14 833 654 796 782 463 910 861
15 317 655 484 783 726 911 977
16 712 656 692 784 961 912 875
17 235 657 912 785 843 913 919
18 602 658 430 786 490 914 639
19 343 659 606 787 631 915 758
20 543 660 716 788 729 916 948
21 372 661 488 789 700 917 862
22 654 662 810 790 382 918 761
23 222 663 459 791 741 919 508
24 614 664 838 792 845 920 972
25 426 665 667 793 920 921 923
26 775 666 239 794 471 922 877
27 433 667 817 795 822 923 952
28 559 668 621 796 851 924 886
29 237 669 378 797 730 925 935
30 898 670 837 798 497 926 978
31 617 671 722 799 880 927 762
32 347 672 437 800 742 928 503
33 808 673 696 801 443 929 883
34 243 674 461 802 903 930 703
35 720 675 737 803 687 931 993
36 454 676 679 804 825 932 925
37 665 677 380 805 500 933 878
38 318 678 812 806 445 934 980
39 604 679 627 807 932 935 941
40 376 680 247 808 846 936 764
41 661 681 899 809 635 937 495
42 428 682 841 810 745 938 926
43 779 683 441 811 826 939 885
44 238 684 622 812 732 940 994
45 675 685 928 813 446 941 735
46 359 686 351 814 962 942 939
47 836 687 724 815 936 943 984
48 458 688 783 816 475 944 967
49 625 689 469 817 853 945 889
50 399 690 629 818 867 946 947
51 662 691 818 819 637 947 831
52 677 692 438 820 907 948 507
53 434 693 669 821 487 949 942
54 567 694 462 822 695 950 751
55 457 695 738 823 746 951 973
56 816 696 683 824 828 952 996
57 245 697 251 825 753 953 890
58 618 698 842 826 854 954 949
59 349 699 849 827 857 955 759
60 787 700 496 828 915 956 892
61 127 701 901 829 964 957 971
62 781 702 820 830 477 958 1000
63 897 703 728 831 909 959 953
64 407 704 467 832 719 960 509
65 666 705 633 833 799 961 863
66 436 706 902 834 699 962 981
67 591 707 367 835 493 963 950
68 363 708 670 836 504 964 974
69 620 709 791 837 748 965 763
70 465 710 442 838 944 966 1008
71 736 711 844 839 858 967 979
72 350 712 630 840 873 968 879
73 678 713 474 841 638 969 954
74 571 714 685 842 754 970 986
75 246 715 850 843 255 971 995
76 681 716 483 844 968 972 891
77 249 717 691 845 869 973 927
78 626 718 711 846 491 974 510
79 460 719 379 847 478 975 765
80 707 720 865 848 383 976 956
81 840 721 795 849 910 977 997
82 411 722 415 850 815 978 982
83 782 723 824 851 917 979 887
84 365 724 960 852 727 980 985
85 789 725 740 853 870 981 943
86 440 726 253 854 701 982 998
87 599 727 905 855 931 983 1001
88 374 728 634 856 860 984 766
89 668 729 444 857 499 985 988
90 628 730 693 858 756 986 951
91 423 731 744 859 731 987 1004
92 900 732 485 860 823 988 893
93 466 733 807 861 922 989 1010
94 848 734 686 862 874 990 957
95 803 735 906 863 976 991 975
96 250 736 470 864 918 992 511
97 790 737 575 865 502 993 1002
98 371 738 715 866 933 994 894
99 709 739 375 867 743 995 983
100 191 740 866 868 760 996 1009
101 573 741 913 869 881 997 955
102 689 742 473 870 494 998 987
103 481 743 852 871 702 999 1012
104 682 744 636 872 921 1000 958
105 413 745 797 873 876 1001 999
106 603 746 431 874 501 1002 1005
107 793 747 694 875 847 1003 989
108 366 748 811 876 992 1004 1016
109 713 749 486 877 447 1005 990
110 468 750 752 878 733 1006 1011
111 710 751 723 879 827 1007 767
112 373 752 798 880 882 1008 1003
113 574 753 489 881 934 1009 1014
114 655 754 856 882 963 1010 1006
115 427 755 908 883 505 1011 1017
116 806 756 254 884 937 1012 895
117 414 757 717 885 747 1013 1013
118 684 758 607 886 855 1014 991
119 904 759 930 887 924 1015 1018
120 252 760 476 888 734 1016 959
121 615 761 697 889 829 1017 1020
122 482 762 725 890 965 1018 1015
123 632 763 914 891 938 1019 1007
124 805 764 439 892 884 1020 1019
125 429 765 819 893 506 1021 1021
126 794 766 839 894 749 1022 1022
127 864 767 868 895 945 1023 1023
Sequence Q2, having a sequence length of 512:
[0, 1, 4, 8, 2, 16, 32, 6, 64, 3, 12, 5, 18, 128, 9, 33, 17, 10, 256, 20, 34, 24, 65, 7, 36, 66, 129, 11, 40, 19, 132, 13, 68, 48, 14, 72, 257, 21, 130, 26, 35, 80, 258, 136, 38, 22, 260, 37, 25, 96, 67, 264, 41, 144, 28, 69, 49, 74, 160, 42, 272, 192, 70, 44, 131, 81, 15, 288, 50, 134, 73, 23, 52, 320, 133, 76, 82, 137, 56, 27, 259, 97, 39, 384, 138, 84, 29, 261, 145, 43, 98, 140, 30, 88, 262, 146, 71, 265, 161, 45, 100, 148, 51, 46, 75, 266, 104, 273, 164, 193, 53, 162, 268, 77, 152, 274, 54, 83, 57, 112, 85, 135, 289, 194, 78, 290, 58, 276, 168, 99, 139, 196, 86, 176, 60, 89, 280, 101, 147, 292, 141, 321, 142, 90, 200, 31, 102, 263, 105, 322, 149, 296, 47, 92, 208, 267, 385, 324, 304, 163, 153, 150, 106, 55, 165, 386, 328, 269, 113, 154, 79, 224, 166, 275, 108, 270, 59, 114, 195, 169, 156, 87, 61, 277, 291, 278, 116, 170, 197, 177, 281, 91, 201, 388, 293, 198, 62, 143, 336, 172, 282, 120, 103, 178, 294, 202, 93, 323, 392, 297, 151, 209, 284, 180, 107, 94, 204, 298, 352, 325, 155, 109, 400, 305, 300, 210, 184, 326, 115, 167, 157, 225, 306, 329, 110, 212, 117, 171, 330, 226, 387, 308, 158, 416, 337, 216, 271, 118, 279, 332, 389, 173, 121, 199, 179, 228, 338, 312, 390, 174, 393, 283, 122, 63, 340, 448, 353, 394, 232, 203, 295, 285, 181, 124, 205, 240, 286, 299, 354, 182, 401, 211, 396, 344, 95, 185, 206, 327, 402, 186, 356, 307, 418, 213, 301, 227, 302, 360, 111, 417, 214, 404, 309, 188, 449, 331, 217, 159, 119, 229, 333, 408, 310, 420, 218, 368, 230, 391, 175, 313, 339, 334, 123, 233, 314, 341, 450, 220, 424, 355, 125, 234, 183, 395, 241, 316, 342, 345, 403, 287, 397, 452, 432, 187, 357, 207, 236, 346, 361, 126, 242, 405, 215, 398, 303, 358, 419, 456, 348, 244, 189, 219, 311, 362, 464, 406, 421, 248, 190, 369, 409, 410, 480, 231, 315, 364, 422, 335, 370, 221, 451, 425, 412, 453, 317, 235, 343, 372, 222, 426, 433, 237, 347, 243, 454, 318, 376, 428, 238, 359, 458, 399, 434, 457, 245, 349, 127, 407, 436, 363, 465, 350, 246, 249, 460, 411, 365, 440, 374, 423, 466, 250, 371, 191, 481, 413, 366, 468, 373, 427, 414, 252, 482, 429, 223, 455, 472, 377, 435, 319, 484, 430, 488, 459, 239, 378, 437, 461, 380, 247, 441, 351, 469, 438, 462, 251, 496, 467, 367, 442, 474, 483, 379, 415, 253, 444, 485, 470, 375, 473, 431, 486, 489, 254, 476, 439, 492, 381, 498, 463, 490, 382, 471, 497, 443, 500, 445, 446, 475, 487, 477, 493, 504, 255, 491, 478, 383, 499, 502, 494, 501, 447, 505, 506, 479, 508, 503, 495, 507, 509, 510, 511]
TABLE Q2
having a sequence length of 512:
Reliability or sequence Polarized channel
number of reliability sequence number
0 0
1 1
2 4
3 8
4 2
5 16
6 32
7 6
8 64
9 3
10 12
11 5
12 18
13 128
14 9
15 33
16 17
17 10
18 256
19 20
20 34
21 24
22 65
23 7
24 36
25 66
26 129
27 11
28 40
29 19
30 132
31 13
32 68
33 48
34 14
35 72
36 257
37 21
38 130
39 26
40 35
41 80
42 258
43 136
44 38
45 22
46 260
47 37
48 25
49 96
50 67
51 264
52 41
53 144
54 28
55 69
56 49
57 74
58 160
59 42
60 272
61 192
62 70
63 44
64 131
65 81
66 15
67 288
68 50
69 134
70 73
71 23
72 52
73 320
74 133
75 76
76 82
77 137
78 56
79 27
80 259
81 97
82 39
83 384
84 138
85 84
86 29
87 261
88 145
89 43
90 98
91 140
92 30
93 88
94 262
95 146
96 71
97 265
98 161
99 45
100 100
101 148
102 51
103 46
104 75
105 266
106 104
107 273
108 164
109 193
110 53
111 162
112 268
113 77
114 152
115 274
116 54
117 83
118 57
119 112
120 85
121 135
122 289
123 194
124 78
125 290
126 58
127 276
128 168
129 99
130 139
131 196
132 86
133 176
134 60
135 89
136 280
137 101
138 147
139 292
140 141
141 321
142 142
143 90
144 200
145 31
146 102
147 263
148 105
149 322
150 149
151 296
152 47
153 92
154 208
155 267
156 385
157 324
158 304
159 163
160 153
161 150
162 106
163 55
164 165
165 386
166 328
167 269
168 113
169 154
170 79
171 224
172 166
173 275
174 108
175 270
176 59
177 114
178 195
179 169
180 156
181 87
182 61
183 277
184 291
185 278
186 116
187 170
188 197
189 177
190 281
191 91
192 201
193 388
194 293
195 198
196 62
197 143
198 336
199 172
200 282
201 120
202 103
203 178
204 294
205 202
206 93
207 323
208 392
209 297
210 151
211 209
212 284
213 180
214 107
215 94
216 204
217 298
218 352
219 325
220 155
221 109
222 400
223 305
224 300
225 210
226 184
227 326
228 115
229 167
230 157
231 225
232 306
233 329
234 110
235 212
236 117
237 171
238 330
239 226
240 387
241 308
242 158
243 416
244 337
245 216
246 271
247 118
248 279
249 332
250 389
251 173
252 121
253 199
254 179
255 228
256 338
257 312
258 390
259 174
260 393
261 283
262 122
263 63
264 340
265 448
266 353
267 394
268 232
269 203
270 295
271 285
272 181
273 124
274 205
275 240
276 286
277 299
278 354
279 182
280 401
281 211
282 396
283 344
284 95
285 185
286 206
287 327
288 402
289 186
290 356
291 307
292 418
293 213
294 301
295 227
296 302
297 360
298 111
299 417
300 214
301 404
302 309
303 188
304 449
305 331
306 217
307 159
308 119
309 229
310 333
311 408
312 310
313 420
314 218
315 368
316 230
317 391
318 175
319 313
320 339
321 334
322 123
323 233
324 314
325 341
326 450
327 220
328 424
329 355
330 125
331 234
332 183
333 395
334 241
335 316
336 342
337 345
338 403
339 287
340 397
341 452
342 432
343 187
344 357
345 207
346 236
347 346
348 361
349 126
350 242
351 405
352 215
353 398
354 303
355 358
356 419
357 456
358 348
359 244
360 189
361 219
362 311
363 362
364 464
365 406
366 421
367 248
368 190
369 369
370 409
371 410
372 480
373 231
374 315
375 364
376 422
377 335
378 370
379 221
380 451
381 425
382 412
383 453
384 317
385 235
386 343
387 372
388 222
389 426
390 433
391 237
392 347
393 243
394 454
395 318
396 376
397 428
398 238
399 359
400 458
401 399
402 434
403 457
404 245
405 349
406 127
407 407
408 436
409 363
410 465
411 350
412 246
413 249
414 460
415 411
416 365
417 440
418 374
419 423
420 466
421 250
422 371
423 191
424 481
425 413
426 366
427 468
428 373
429 427
430 414
431 252
432 482
433 429
434 223
435 455
436 472
437 377
438 435
439 319
440 484
441 430
442 488
443 459
444 239
445 378
446 437
447 461
448 380
449 247
450 441
451 351
452 469
453 438
454 462
455 251
456 496
457 467
458 367
459 442
460 474
461 483
462 379
463 415
464 253
465 444
466 485
467 470
468 375
469 473
470 431
471 486
472 489
473 254
474 476
475 439
476 492
477 381
478 498
479 463
480 490
481 382
482 471
483 497
484 443
485 500
486 445
487 446
488 475
489 487
490 477
491 493
492 504
493 255
494 491
495 478
496 383
497 499
498 502
499 494
500 501
501 447
502 505
503 506
504 479
505 508
506 503
507 495
508 507
509 509
510 510
511 511
Sequence Q3, having a sequence length of 256:
[0, 1, 4, 8, 2, 16, 32, 6, 64, 3, 12, 5, 18, 128, 9, 33, 17, 10, 20, 34, 24, 65, 7, 36, 66, 129, 11, 40, 19, 132, 13, 68, 48, 14, 72, 21, 130, 26, 35, 80, 136, 38, 22, 37, 25, 96, 67, 41, 144, 28, 69, 49, 74, 160, 42, 192, 70, 44, 131, 81, 15, 50, 134, 73, 23, 52, 133, 76, 82, 137, 56, 27, 97, 39, 138, 84, 29, 145, 43, 98, 140, 30, 88, 146, 71, 161, 45, 100, 148, 51, 46, 75, 104, 164, 193, 53, 162, 77, 152, 54, 83, 57, 112, 85, 135, 194, 78, 58, 168, 99, 139, 196, 86, 176, 60, 89, 101, 147, 141, 142, 90, 200, 31, 102, 105, 149, 47, 92, 208, 163, 153, 150, 106, 55, 165, 113, 154, 79, 224, 166, 108, 59, 114, 195, 169, 156, 87, 61, 116, 170, 197, 177, 91, 201, 198, 62, 143, 172, 120, 103, 178, 202, 93, 151, 209, 180, 107, 94, 204, 155, 109, 210, 184, 115, 167, 157, 225, 110, 212, 117, 171, 226, 158, 216, 118, 173, 121, 199, 179, 228, 174, 122, 63, 232, 203, 181, 124, 205, 240, 182, 211, 95, 185, 206, 186, 213, 227, 111, 214, 188, 217, 159, 119, 229, 218, 230, 175, 123, 233, 220, 125, 234, 183, 241, 187, 207, 236, 126, 242, 215, 244, 189, 219, 248, 190, 231, 221, 235, 222, 237, 243, 238, 245, 127, 246, 249, 250, 191, 252, 223, 239, 247, 251, 253, 254, 255]
TABLE Q3
having a sequence length of 256:
Reliability or sequence Polarized channel
number of reliability sequence number
0 0
1 1
2 4
3 8
4 2
5 16
6 32
7 6
8 64
9 3
10 12
11 5
12 18
13 128
14 9
15 33
16 17
17 10
18 20
19 34
20 24
21 65
22 7
23 36
24 66
25 129
26 11
27 40
28 19
29 132
30 13
31 68
32 48
33 14
34 72
35 21
36 130
37 26
38 35
39 80
40 136
41 38
42 22
43 37
44 25
45 96
46 67
47 41
48 144
49 28
50 69
51 49
52 74
53 160
54 42
55 192
56 70
57 44
58 131
59 81
60 15
61 50
62 134
63 73
64 23
65 52
66 133
67 76
68 82
69 137
70 56
71 27
72 97
73 39
74 138
75 84
76 29
77 145
78 43
79 98
80 140
81 30
82 88
83 146
84 71
85 161
86 45
87 100
88 148
89 51
90 46
91 75
92 104
93 164
94 193
95 53
96 162
97 77
98 152
99 54
100 83
101 57
102 112
103 85
104 135
105 194
106 78
107 58
108 168
109 99
110 139
111 196
112 86
113 176
114 60
115 89
116 101
117 147
118 141
119 142
120 90
121 200
122 31
123 102
124 105
125 149
126 47
127 92
128 208
129 163
130 153
131 150
132 106
133 55
134 165
135 113
136 154
137 79
138 224
139 166
140 108
141 59
142 114
143 195
144 169
145 156
146 87
147 61
148 116
149 170
150 197
151 177
152 91
153 201
154 198
155 62
156 143
157 172
158 120
159 103
160 178
161 202
162 93
163 151
164 209
165 180
166 107
167 94
168 204
169 155
170 109
171 210
172 184
173 115
174 167
175 157
176 225
177 110
178 212
179 117
180 171
181 226
182 158
183 216
184 118
185 173
186 121
187 199
188 179
189 228
190 174
191 122
192 63
193 232
194 203
195 181
196 124
197 205
198 240
199 182
200 211
201 95
202 185
203 206
204 186
205 213
206 227
207 111
208 214
209 188
210 217
211 159
212 119
213 229
214 218
215 230
216 175
217 123
218 233
219 220
220 125
221 234
222 183
223 241
224 187
225 207
226 236
227 126
228 242
229 215
230 244
231 189
232 219
233 248
234 190
235 231
236 221
237 235
238 222
239 237
240 243
241 238
242 245
243 127
244 246
245 249
246 250
247 191
248 252
249 223
250 239
251 247
252 251
253 253
254 254
255 255
Sequence Q4, having a sequence length of 128:
[0, 1, 4, 8, 2, 16, 32, 6, 64, 3, 12, 5, 18, 9, 33, 17, 10, 20, 34, 24, 65, 7, 36, 66, 11, 40, 19, 13, 68, 48, 14, 72, 21, 26, 35, 80, 38, 22, 37, 25, 96, 67, 41, 28, 69, 49, 74, 42, 70, 44, 81, 15, 50, 73, 23, 52, 76, 82, 56, 27, 97, 39, 84, 29, 43, 98, 30, 88, 71, 45, 100, 51, 46, 75, 104, 53, 77, 54, 83, 57, 112, 85, 78, 58, 99, 86, 60, 89, 101, 90, 31, 102, 105, 47, 92, 106, 55, 113, 79, 108, 59, 114, 87, 61, 116, 91, 62, 120, 103, 93, 107, 94, 109, 115, 110, 117, 118, 121, 122, 63, 124, 95, 111, 119, 123, 125, 126, 127]
TABLE Q4
having a sequence length of 128:
Reliability or sequence Polarized channel
number of reliability sequence number
0 0
1 1
2 4
3 8
4 2
5 16
6 32
7 6
8 64
9 3
10 12
11 5
12 18
13 9
14 33
15 17
16 10
17 20
18 34
19 24
20 65
21 7
22 36
23 66
24 11
25 40
26 19
27 13
28 68
29 48
30 14
31 72
32 21
33 26
34 35
35 80
36 38
37 22
38 37
39 25
40 96
41 67
42 41
43 28
44 69
45 49
46 74
47 42
48 70
49 44
50 81
51 15
52 50
53 73
54 23
55 52
56 76
57 82
58 56
59 27
60 97
61 39
62 84
63 29
64 43
65 98
66 30
67 88
68 71
69 45
70 100
71 51
72 46
73 75
74 104
75 53
76 77
77 54
78 83
79 57
80 112
81 85
82 78
83 58
84 99
85 86
86 60
87 89
88 101
89 90
90 31
91 102
92 105
93 47
94 92
95 106
96 55
97 113
98 79
99 108
100 59
101 114
102 87
103 61
104 116
105 91
106 62
107 120
108 103
109 93
110 107
111 94
112 109
113 115
114 110
115 117
116 118
117 121
118 122
119 63
120 124
121 95
122 111
123 119
124 123
125 125
126 126
127 127
Sequence Q5, having a sequence length of 64:
[0, 1, 4, 8, 2, 16, 32, 6, 3, 12, 5, 18, 9, 33, 17, 10, 20, 34, 24, 7, 36, 11, 40, 19, 13, 48, 14, 21, 26, 35, 38, 22, 37, 25, 41, 28, 49, 42, 44, 15, 50, 23, 52, 56, 27, 39, 29, 43, 30, 45, 51, 46, 53, 54, 57, 58, 60, 31, 47, 55, 59, 61, 62, 63]
TABLE Q5
having a sequence length of 64:
Reliability or sequence Polarized channel
number of reliability sequence number
0 0
1 1
2 4
3 8
4 2
5 16
6 32
7 6
8 3
9 12
10 5
11 18
12 9
13 33
14 17
15 10
16 20
17 34
18 24
19 7
20 36
21 11
22 40
23 19
24 13
25 48
26 14
27 21
28 26
29 35
30 38
31 22
32 37
33 25
34 41
35 28
36 49
37 42
38 44
39 15
40 50
41 23
42 52
43 56
44 27
45 39
46 29
47 43
48 30
49 45
50 51
51 46
52 53
53 54
54 57
55 58
56 60
57 31
58 47
59 55
60 59
61 61
62 62
63 63
Sequence Z1, having a sequence length of 1024:
[0, 1, 4, 10, 2, 12, 7, 24, 3, 15, 18, 28, 11, 33, 36, 70, 5, 17, 13, 30, 20, 39, 47, 76, 22, 51, 41, 84, 57, 92, 99, 161, 6, 16, 21, 42, 25, 50, 46, 88, 29, 55, 62, 96, 67, 107, 111, 169, 35, 59, 72, 110, 77, 119, 126, 184, 83, 129, 138, 200, 148, 207, 225, 322, 8, 23, 26, 53, 34, 58, 66, 103, 37, 74, 60, 113, 80, 123, 136, 193, 43, 69, 81, 128, 91, 131, 145, 205, 100, 149, 158, 218, 171, 238, 250, 355, 52, 87, 97, 142, 108, 151, 162, 233, 115, 164, 183, 249, 197, 258, 276, 377, 130, 191, 201, 268, 212, 279, 295, 394, 231, 302, 318, 415, 338, 430, 463, 573, 14, 27, 40, 68, 31, 79, 73, 132, 45, 82, 90, 143, 98, 155, 157, 226, 56, 94, 102, 152, 109, 167, 182, 243, 124, 181, 192, 257, 204, 271, 287, 389, 61, 106, 121, 180, 117, 185, 195, 269, 140, 203, 213, 280, 229, 300, 313, 410, 146, 216, 234, 305, 247, 337, 347, 432, 265, 356, 363, 451, 385, 481, 497, 612, 65, 118, 135, 202, 144, 214, 223, 303, 159, 220, 237, 331, 251, 339, 357, 453, 172, 245, 264, 349, 278, 370, 382, 467, 292, 388, 405, 483, 425, 517, 535, 640, 194, 272, 283, 372, 306, 395, 407, 507, 330, 418, 431, 529, 459, 541, 556, 666, 340, 434, 464, 546, 479, 569, 587, 680, 495, 589, 608, 697, 632, 726, 756, 843, 19, 38, 44, 85, 48, 93, 101, 163, 54, 105, 114, 173, 122, 190, 199, 293, 64, 116, 125, 196, 139, 208, 211, 296, 150, 217, 230, 316, 246, 336, 344, 444, 71, 133, 137, 209, 153, 222, 235, 335, 168, 242, 253, 345, 262, 371, 373, 470, 176, 261, 273, 367, 286, 384, 402, 485, 310, 411, 419, 509, 438, 527, 550, 653, 78, 156, 166, 239, 175, 255, 266, 358, 188, 275, 282, 387, 298, 396, 414, 513, 227, 290, 308, 412, 323, 422, 439, 531, 351, 440, 460, 544, 478, 571, 584, 686, 254, 327, 346, 427, 364, 452, 472, 558, 376, 462, 487, 580, 511, 596, 620, 707, 406, 499, 515, 610, 533, 624, 600, 739, 552, 647, 669, 719, 677, 771, 790, 848, 89, 174, 186, 285, 221, 299, 312, 409, 241, 315, 329, 433, 350, 445, 468, 562, 260, 348, 361, 443, 383, 466, 491, 576, 397, 501, 503, 594, 523, 617, 629, 722, 289, 380, 369, 474, 403, 493, 512, 603, 426, 521, 537, 627, 554, 637, 658, 746, 450, 539, 565, 650, 578, 672, 692, 764, 598, 683, 710, 801, 729, 806, 813, 877, 325, 386, 424, 519, 446, 525, 548, 642, 476, 567, 560, 663, 591, 674, 694, 782, 489, 582, 605, 704, 622, 689, 736, 794, 645, 742, 713, 816, 760, 830, 847, 898, 505, 615, 634, 716, 655, 732, 749, 821, 661, 753, 786, 846, 768, 835, 870, 937, 700, 798, 775, 857, 805, 874, 865, 928, 836, 883, 893, 948, 919, 960, 974, 992, 9, 32, 75, 120, 49, 134, 104, 210, 63, 154, 170, 224, 127, 248, 256, 332, 86, 165, 141, 236, 179, 259, 291, 360, 177, 297, 267, 381, 311, 398, 413, 532, 95, 160, 206, 274, 189, 294, 281, 392, 219, 307, 320, 416, 334, 435, 448, 540, 240, 326, 343, 442, 354, 461, 469, 566, 366, 480, 498, 586, 508, 613, 625, 737, 112, 187, 198, 301, 244, 314, 333, 429, 228, 342, 352, 455, 365, 465, 482, 579, 270, 362, 375, 488, 391, 471, 496, 599, 404, 520, 530, 618, 551, 648, 659, 758, 288, 390, 400, 518, 421, 506, 536, 633, 437, 543, 570, 649, 581, 668, 684, 773, 475, 561, 590, 679, 602, 690, 712, 787, 635, 705, 728, 809, 744, 819, 841, 914, 147, 215, 263, 341, 232, 359, 368, 484, 284, 378, 393, 500, 408, 524, 534, 626, 309, 401, 420, 510, 436, 553, 563, 651, 454, 549, 577, 665, 601, 693, 708, 779, 319, 428, 447, 557, 458, 564, 585, 676, 492, 588, 616, 696, 630, 714, 734, 803, 514, 614, 641, 717, 656, 730, 747, 822, 673, 761, 770, 834, 789, 854, 871, 930, 324, 457, 486, 592, 504, 611, 623, 718, 528, 621, 643, 738, 660, 757, 769, 832, 547, 652, 671, 751, 687, 762, 783, 852, 703, 788, 797, 859, 812, 878, 888, 941, 583, 675, 695, 777, 725, 791, 800, 867, 731, 810, 823, 885, 837, 894, 903, 950, 750, 825, 842, 897, 858, 907, 915, 955, 868, 918, 927, 965, 936, 975, 984, 1007, 178, 252, 277, 379, 317, 399, 417, 538, 304, 423, 441, 555, 456, 574, 595, 688, 321, 449, 477, 572, 494, 597, 609, 709, 516, 619, 638, 721, 654, 745, 752, 833, 328, 473, 490, 607, 522, 636, 628, 733, 545, 646, 662, 748, 678, 772, 774, 850, 568, 667, 691, 765, 702, 781, 795, 860, 723, 804, 811, 879, 824, 889, 900, 947, 353, 526, 502, 644, 559, 670, 664, 766, 593, 682, 698, 785, 711, 792, 808, 875, 606, 699, 715, 796, 743, 817, 826, 886, 754, 827, 839, 896, 856, 910, 917, 961, 639, 720, 740, 818, 767, 845, 853, 904, 776, 840, 862, 912, 873, 922, 933, 968, 799, 869, 880, 929, 892, 939, 924, 979, 901, 945, 953, 972, 956, 988, 994, 1012, 374, 575, 542, 681, 604, 701, 706, 802, 631, 727, 735, 820, 755, 831, 849, 906, 657, 741, 763, 828, 780, 851, 864, 913, 793, 872, 861, 921, 887, 932, 938, 973, 685, 778, 759, 855, 807, 866, 881, 925, 815, 884, 891, 942, 902, 935, 949, 981, 838, 895, 908, 946, 916, 954, 963, 986, 923, 959, 969, 997, 976, 990, 1000, 1016, 724, 784, 814, 882, 829, 890, 899, 944, 844, 909, 905, 957, 920, 951, 964, 991, 863, 911, 926, 967, 934, 962, 978, 995, 943, 980, 970, 998, 985, 1003, 1005, 1014, 876, 931, 940, 971, 952, 977, 982, 1001, 958, 983, 993, 1008, 987, 1002, 1010, 1019, 966, 996, 989, 1006, 999, 1013, 1009, 1018, 1004, 1011, 1015, 1020, 1017, 1021, 1022, 1023]
TABLE Z1
having a sequence length of 1024:
Polarized channel Reliability or sequence
sequence number number of reliability
0 0
1 1
2 4
3 10
4 2
5 12
6 7
7 24
8 3
9 15
10 18
11 28
12 11
13 33
14 36
15 70
16 5
17 17
18 13
19 30
20 20
21 39
22 47
23 76
24 22
25 51
26 41
27 84
28 57
29 92
30 99
31 161
32 6
33 16
34 21
35 42
36 25
37 50
38 46
39 88
40 29
41 55
42 62
43 96
44 67
45 107
46 111
47 169
48 35
49 59
50 72
51 110
52 77
53 119
54 126
55 184
56 83
57 129
58 138
59 200
60 148
61 207
62 225
63 322
64 8
65 23
66 26
67 53
68 34
69 58
70 66
71 103
72 37
73 74
74 60
75 113
76 80
77 123
78 136
79 193
80 43
81 69
82 81
83 128
84 91
85 131
86 145
87 205
88 100
89 149
90 158
91 218
92 171
93 238
94 250
95 355
96 52
97 87
98 97
99 142
100 108
101 151
102 162
103 233
104 115
105 164
106 183
107 249
108 197
109 258
110 276
111 377
112 130
113 191
114 201
115 268
116 212
117 279
118 295
119 394
120 231
121 302
122 318
123 415
124 338
125 430
126 463
127 573
128 14
129 27
130 40
131 68
132 31
133 79
134 73
135 132
136 45
137 82
138 90
139 143
140 98
141 155
142 157
143 226
144 56
145 94
146 102
147 152
148 109
149 167
150 182
151 243
152 124
153 181
154 192
155 257
156 204
157 271
158 287
159 389
160 61
161 106
162 121
163 180
164 117
165 185
166 195
167 269
168 140
169 203
170 213
171 280
172 229
173 300
174 313
175 410
176 146
177 216
178 234
179 305
180 247
181 337
182 347
183 432
184 265
185 356
186 363
187 451
188 385
189 481
190 497
191 612
192 65
193 118
194 135
195 202
196 144
197 214
198 223
199 303
200 159
201 220
202 237
203 331
204 251
205 339
206 357
207 453
208 172
209 245
210 264
211 349
212 278
213 370
214 382
215 467
216 292
217 388
218 405
219 483
220 425
221 517
222 535
223 640
224 194
225 272
226 283
227 372
228 306
229 395
230 407
231 507
232 330
233 418
234 431
235 529
236 459
237 541
238 556
239 666
240 340
241 434
242 464
243 546
244 479
245 569
246 587
247 680
248 495
249 589
250 608
251 697
252 632
253 726
254 756
255 843
256 19
257 38
258 44
259 85
260 48
261 93
262 101
263 163
264 54
265 105
266 114
267 173
268 122
269 190
270 199
271 293
272 64
273 116
274 125
275 196
276 139
277 208
278 211
279 296
280 150
281 217
282 230
283 316
284 246
285 336
286 344
287 444
288 71
289 133
290 137
291 209
292 153
293 222
294 235
295 335
296 168
297 242
298 253
299 345
300 262
301 371
302 373
303 470
304 176
305 261
306 273
307 367
308 286
309 384
310 402
311 485
312 310
313 411
314 419
315 509
316 438
317 527
318 550
319 653
320 78
321 156
322 166
323 239
324 175
325 255
326 266
327 358
328 188
329 275
330 282
331 387
332 298
333 396
334 414
335 513
336 227
337 290
338 308
339 412
340 323
341 422
342 439
343 531
344 351
345 440
346 460
347 544
348 478
349 571
350 584
351 686
352 254
353 327
354 346
355 427
356 364
357 452
358 472
359 558
360 376
361 462
362 487
363 580
364 511
365 596
366 620
367 707
368 406
369 499
370 515
371 610
372 533
373 624
374 600
375 739
376 552
377 647
378 669
379 719
380 677
381 771
382 790
383 848
384 89
385 174
386 186
387 285
388 221
389 299
390 312
391 409
392 241
393 315
394 329
395 433
396 350
397 445
398 468
399 562
400 260
401 348
402 361
403 443
404 383
405 466
406 491
407 576
408 397
409 501
410 503
411 594
412 523
413 617
414 629
415 722
416 289
417 380
418 369
419 474
420 403
421 493
422 512
423 603
424 426
425 521
426 537
427 627
428 554
429 637
430 658
431 746
432 450
433 539
434 565
435 650
436 578
437 672
438 692
439 764
440 598
441 683
442 710
443 801
444 729
445 806
446 813
447 877
448 325
449 386
450 424
451 519
452 446
453 525
454 548
455 642
456 476
457 567
458 560
459 663
460 591
461 674
462 694
463 782
464 489
465 582
466 605
467 704
468 622
469 689
470 736
471 794
472 645
473 742
474 713
475 816
476 760
477 830
478 847
479 898
480 505
481 615
482 634
483 716
484 655
485 732
486 749
487 821
488 661
489 753
490 786
491 846
492 768
493 835
494 870
495 937
496 700
497 798
498 775
499 857
500 805
501 874
502 865
503 928
504 836
505 883
506 893
507 948
508 919
509 960
510 974
511 992
512 9
513 32
514 75
515 120
516 49
517 134
518 104
519 210
520 63
521 154
522 170
523 224
524 127
525 248
526 256
527 332
528 86
529 165
530 141
531 236
532 179
533 259
534 291
535 360
536 177
537 297
538 267
539 381
540 311
541 398
542 413
543 532
544 95
545 160
546 206
547 274
548 189
549 294
550 281
551 392
552 219
553 307
554 320
555 416
556 334
557 435
558 448
559 540
560 240
561 326
562 343
563 442
564 354
565 461
566 469
567 566
568 366
569 480
570 498
571 586
572 508
573 613
574 625
575 737
576 112
577 187
578 198
579 301
580 244
581 314
582 333
583 429
584 228
585 342
586 352
587 455
588 365
589 465
590 482
591 579
592 270
593 362
594 375
595 488
596 391
597 471
598 496
599 599
600 404
601 520
602 530
603 618
604 551
605 648
606 659
607 758
608 288
609 390
610 400
611 518
612 421
613 506
614 536
615 633
616 437
617 543
618 570
619 649
620 581
621 668
622 684
623 773
624 475
625 561
626 590
627 679
628 602
629 690
630 712
631 787
632 635
633 705
634 728
635 809
636 744
637 819
638 841
639 914
640 147
641 215
642 263
643 341
644 232
645 359
646 368
647 484
648 284
649 378
650 393
651 500
652 408
653 524
654 534
655 626
656 309
657 401
658 420
659 510
660 436
661 553
662 563
663 651
664 454
665 549
666 577
667 665
668 601
669 693
670 708
671 779
672 319
673 428
674 447
675 557
676 458
677 564
678 585
679 676
680 492
681 588
682 616
683 6%
684 630
685 714
686 734
687 803
688 514
689 614
690 641
691 717
692 656
693 730
694 747
695 822
696 673
697 761
698 770
699 834
700 789
701 854
702 871
703 930
704 324
705 457
706 486
707 592
708 504
709 611
710 623
711 718
712 528
713 621
714 643
715 738
716 660
717 757
718 769
719 832
720 547
721 652
722 671
723 751
724 687
725 762
726 783
727 852
728 703
729 788
730 797
731 859
732 812
733 878
734 888
735 941
736 583
737 675
738 695
739 777
740 725
741 791
742 800
743 867
744 731
745 810
746 823
747 885
748 837
749 894
750 903
751 950
752 750
753 825
754 842
755 897
756 858
757 907
758 915
759 955
760 868
761 918
762 927
763 965
764 936
765 975
766 984
767 1007
768 178
769 252
770 277
771 379
772 317
773 399
774 417
775 538
776 304
777 423
778 441
779 555
780 456
781 574
782 595
783 688
784 321
785 449
786 477
787 572
788 494
789 597
790 609
791 709
792 516
793 619
794 638
795 721
796 654
797 745
798 752
799 833
800 328
801 473
802 490
803 607
804 522
805 636
806 628
807 733
808 545
809 646
810 662
811 748
812 678
813 772
814 774
815 850
816 568
817 667
818 691
819 765
820 702
821 781
822 795
823 860
824 723
825 804
826 811
827 879
828 824
829 889
830 900
831 947
832 353
833 526
834 502
835 644
836 559
837 670
838 664
839 766
840 593
841 682
842 698
843 785
844 711
845 792
846 808
847 875
848 606
849 699
850 715
851 796
852 743
853 817
854 826
855 886
856 754
857 827
858 839
859 896
860 856
861 910
862 917
863 961
864 639
865 720
866 740
867 818
868 767
869 845
870 853
871 904
872 776
873 840
874 862
875 912
876 873
877 922
878 933
879 968
880 799
881 869
882 880
883 929
884 892
885 939
886 924
887 979
888 901
889 945
890 953
891 972
892 956
893 988
894 994
895 1012
896 374
897 575
898 542
899 681
900 604
901 701
902 706
903 802
904 631
905 727
906 735
907 820
908 755
909 831
910 849
911 906
912 657
913 741
914 763
915 828
916 780
917 851
918 864
919 913
920 793
921 872
922 861
923 921
924 887
925 932
926 938
927 973
928 685
929 778
930 759
931 855
932 807
933 866
934 881
935 925
936 815
937 884
938 891
939 942
940 902
941 935
942 949
943 981
944 838
945 895
946 908
947 946
948 916
949 954
950 963
951 986
952 923
953 959
954 969
955 997
956 976
957 990
958 1000
959 1016
960 724
961 784
962 814
963 882
964 829
965 890
966 899
967 944
968 844
969 909
970 905
971 957
972 920
973 951
974 964
975 991
976 863
977 911
978 926
979 967
980 934
981 962
982 978
983 995
984 943
985 980
986 970
987 998
988 985
989 1003
990 1005
991 1014
992 876
993 931
994 940
995 971
996 952
997 977
998 982
999 1001
1000 958
1001 983
1002 993
1003 1008
1004 987
1005 1002
1006 1010
1007 1019
1008 966
1009 996
1010 989
1011 1006
1012 999
1013 1013
1014 1009
1015 1018
1016 1004
1017 1011
1018 1015
1019 1020
1020 1017
1021 1021
1022 1022
1023 1023
Sequence Z2, having a sequence length of 512:
[0, 1, 4, 9, 2, 11, 7, 23, 3, 14, 17, 27, 10, 31, 34, 66, 5, 16, 12, 29, 19, 37, 45, 71, 21, 48, 39, 79, 54, 86, 92, 145, 6, 15, 20, 40, 24, 47, 44, 82, 28, 52, 59, 89, 63, 99, 103, 152, 33, 56, 68, 102, 72, 110, 116, 163, 78, 118, 126, 176, 134, 182, 196, 263, 8, 22, 25, 50, 32, 55, 62, 96, 35, 70, 57, 104, 75, 113, 124, 170, 41, 65, 76, 117, 85, 120, 132, 181, 93, 135, 143, 191, 153, 206, 215, 284, 49, 81, 90, 129, 100, 137, 146, 202, 106, 148, 162, 214, 174, 221, 234, 298, 119, 168, 177, 228, 186, 236, 247, 308, 201, 252, 262, 322, 273, 330, 349, 406, 13, 26, 38, 64, 30, 74, 69, 121, 43, 77, 84, 130, 91, 140, 142, 197, 53, 88, 95, 138, 101, 150, 161, 210, 114, 160, 169, 220, 180, 230, 242, 307, 58, 98, 111, 159, 108, 164, 172, 229, 128, 179, 187, 237, 199, 251, 259, 318, 133, 189, 203, 254, 213, 272, 279, 332, 226, 285, 289, 343, 303, 360, 368, 423, 61, 109, 123, 178, 131, 188, 195, 253, 144, 192, 205, 269, 216, 274, 286, 345, 154, 211, 225, 281, 235, 293, 300, 352, 245, 306, 314, 361, 327, 379, 388, 434, 171, 231, 239, 295, 255, 309, 316, 373, 268, 323, 331, 385, 346, 391, 398, 444, 275, 334, 350, 393, 359, 404, 412, 449, 367, 413, 421, 455, 431, 464, 473, 493, 18, 36, 42, 80, 46, 87, 94, 147, 51, 97, 105, 155, 112, 167, 175, 246, 60, 107, 115, 173, 127, 183, 185, 248, 136, 190, 200, 261, 212, 271, 276, 339, 67, 122, 125, 184, 139, 194, 204, 270, 151, 209, 217, 277, 224, 294, 296, 354, 158, 223, 232, 291, 241, 302, 312, 362, 257, 319, 324, 374, 335, 384, 395, 439, 73, 141, 149, 207, 157, 219, 227, 287, 166, 233, 238, 305, 249, 310, 321, 377, 198, 244, 256, 320, 264, 325, 336, 386, 283, 337, 347, 392, 358, 405, 411, 451, 218, 266, 278, 329, 290, 344, 355, 399, 297, 348, 363, 409, 375, 416, 426, 458, 315, 369, 378, 422, 387, 428, 418, 468, 396, 437, 445, 462, 448, 477, 481, 496, 83, 156, 165, 240, 193, 250, 258, 317, 208, 260, 267, 333, 282, 340, 353, 401, 222, 280, 288, 338, 301, 351, 365, 407, 311, 370, 371, 415, 382, 425, 430, 463, 243, 299, 292, 356, 313, 366, 376, 419, 328, 381, 389, 429, 397, 433, 441, 470, 342, 390, 402, 438, 408, 446, 453, 475, 417, 450, 459, 484, 465, 486, 487, 501, 265, 304, 326, 380, 341, 383, 394, 435, 357, 403, 400, 443, 414, 447, 454, 479, 364, 410, 420, 457, 427, 452, 467, 482, 436, 469, 460, 488, 474, 490, 495, 504, 372, 424, 432, 461, 440, 466, 471, 489, 442, 472, 480, 494, 476, 491, 499, 507, 456, 483, 478, 497, 485, 500, 498, 506, 492, 502, 503, 508, 505, 509, 510, 511]
TABLE Z2
having a sequence length of 512:
Polarized channel Reliability or sequence
sequence number number of reliability
0 0
1 1
2 4
3 9
4 2
5 11
6 7
7 23
8 3
9 14
10 17
11 27
12 10
13 31
14 34
15 66
16 5
17 16
18 12
19 29
20 19
21 37
22 45
23 71
24 21
25 48
26 39
27 79
28 54
29 86
30 92
31 145
32 6
33 15
34 20
35 40
36 24
37 47
38 44
39 82
40 28
41 52
42 59
43 89
44 63
45 99
46 103
47 152
48 33
49 56
50 68
51 102
52 72
53 110
54 116
55 163
56 78
57 118
58 126
59 176
60 134
61 182
62 196
63 263
64 8
65 22
66 25
67 50
68 32
69 55
70 62
71 %
72 35
73 70
74 57
75 104
76 75
77 113
78 124
79 170
80 41
81 65
82 76
83 117
84 85
85 120
86 132
87 181
88 93
89 135
90 143
91 191
92 153
93 206
94 215
95 284
96 49
97 81
98 90
99 129
100 100
101 137
102 146
103 202
104 106
105 148
106 162
107 214
108 174
109 221
110 234
111 298
112 119
113 168
114 177
115 228
116 186
117 236
118 247
119 308
120 201
121 252
122 262
123 322
124 273
125 330
126 349
127 406
128 13
129 26
130 38
131 64
132 30
133 74
134 69
135 121
136 43
137 77
138 84
139 130
140 91
141 140
142 142
143 197
144 53
145 88
146 95
147 138
148 101
149 150
150 161
151 210
152 114
153 160
154 169
155 220
156 180
157 230
158 242
159 307
160 58
161 98
162 111
163 159
164 108
165 164
166 172
167 229
168 128
169 179
170 187
171 237
172 199
173 251
174 259
175 318
176 133
177 189
178 203
179 254
180 213
181 272
182 279
183 332
184 226
185 285
186 289
187 343
188 303
189 360
190 368
191 423
192 61
193 109
194 123
195 178
196 131
197 188
198 195
199 253
200 144
201 192
202 205
203 269
204 216
205 274
206 286
207 345
208 154
209 211
210 225
211 281
212 235
213 293
214 300
215 352
216 245
217 306
218 314
219 361
220 327
221 379
222 388
223 434
224 171
225 231
226 239
227 295
228 255
229 309
230 316
231 373
232 268
233 323
234 331
235 385
236 346
237 391
238 398
239 444
240 275
241 334
242 350
243 393
244 359
245 404
246 412
247 449
248 367
249 413
250 421
251 455
252 431
253 464
254 473
255 493
256 18
257 36
258 42
259 80
260 46
261 87
262 94
263 147
264 51
265 97
266 105
267 155
268 112
269 167
270 175
271 246
272 60
273 107
274 115
275 173
276 127
277 183
278 185
279 248
280 136
281 190
282 200
283 261
284 212
285 271
286 276
287 339
288 67
289 122
290 125
291 184
292 139
293 194
294 204
295 270
296 151
297 209
298 217
299 277
300 224
301 294
302 296
303 354
304 158
305 223
306 232
307 291
308 241
309 302
310 312
311 362
312 257
313 319
314 324
315 374
316 335
317 384
318 395
319 439
320 73
321 141
322 149
323 207
324 157
325 219
326 227
327 287
328 166
329 233
330 238
331 305
332 249
333 310
334 321
335 377
336 198
337 244
338 256
339 320
340 264
341 325
342 336
343 386
344 283
345 337
346 347
347 392
348 358
349 405
350 411
351 451
352 218
353 266
354 278
355 329
356 290
357 344
358 355
359 399
360 297
361 348
362 363
363 409
364 375
365 416
366 426
367 458
368 315
369 369
370 378
371 422
372 387
373 428
374 418
375 468
376 396
377 437
378 445
379 462
380 448
381 477
382 481
383 496
384 83
385 156
386 165
387 240
388 193
389 250
390 258
391 317
392 208
393 260
394 267
395 333
396 282
397 340
398 353
399 401
400 222
401 280
402 288
403 338
404 301
405 351
406 365
407 407
408 311
409 370
410 371
411 415
412 382
413 425
414 430
415 463
416 243
417 299
418 292
419 356
420 313
421 366
422 376
423 419
424 328
425 381
426 389
427 429
428 397
429 433
430 441
431 470
432 342
433 390
434 402
435 438
436 408
437 446
438 453
439 475
440 417
441 450
442 459
443 484
444 465
445 486
446 487
447 501
448 265
449 304
450 326
451 380
452 341
453 383
454 394
455 435
456 357
457 403
458 400
459 443
460 414
461 447
462 454
463 479
464 364
465 410
466 420
467 457
468 427
469 452
470 467
471 482
472 436
473 469
474 460
475 488
476 474
477 490
478 495
479 504
480 372
481 424
482 432
483 461
484 440
485 466
486 471
487 489
488 442
489 472
490 480
491 494
492 476
493 491
494 499
495 507
496 456
497 483
498 478
499 497
500 485
501 500
502 498
503 506
504 492
505 502
506 503
507 508
508 505
509 509
510 510
511 511
Sequence Z3, having a sequence length of 256:
[0, 1, 4, 9, 2, 11, 7, 22, 3, 14, 17, 26, 10, 30, 33, 60, 5, 16, 12, 28, 18, 35, 42, 64, 20, 44, 37, 71, 49, 76, 81, 122, 6, 15, 19, 38, 23, 43, 41, 73, 27, 47, 54, 78, 57, 86, 90, 126, 32, 51, 61, 89, 65, 95, 99, 133, 70, 101, 107, 141, 114, 147, 155, 192, 8, 21, 24, 46, 31, 50, 56, 84, 34, 63, 52, 91, 67, 97, 106, 137, 39, 59, 68, 100, 75, 103, 112, 146, 82, 115, 120, 152, 127, 162, 167, 201, 45, 72, 79, 109, 87, 116, 123, 159, 92, 124, 132, 166, 140, 170, 177, 207, 102, 135, 142, 173, 148, 179, 184, 212, 158, 186, 191, 217, 196, 220, 227, 243, 13, 25, 36, 58, 29, 66, 62, 104, 40, 69, 74, 110, 80, 118, 119, 156, 48, 77, 83, 117, 88, 125, 131, 163, 98, 130, 136, 169, 145, 175, 182, 211, 53, 85, 96, 129, 93, 134, 139, 174, 108, 144, 149, 180, 157, 185, 190, 216, 113, 151, 160, 188, 165, 195, 199, 222, 172, 202, 204, 224, 209, 231, 234, 247, 55, 94, 105, 143, 111, 150, 154, 187, 121, 153, 161, 194, 168, 197, 203, 225, 128, 164, 171, 200, 178, 205, 208, 229, 183, 210, 214, 232, 219, 236, 238, 249, 138, 176, 181, 206, 189, 213, 215, 235, 193, 218, 221, 237, 226, 239, 241, 250, 198, 223, 228, 240, 230, 242, 244, 251, 233, 245, 246, 252, 248, 253, 254, 255]
TABLE Z3
having a sequence length of 256:
Polarized channel Reliability or sequence
sequence number number of reliability
0 0
1 1
2 4
3 9
4 2
5 11
6 7
7 22
8 3
9 14
10 17
11 26
12 10
13 30
14 33
15 60
16 5
17 16
18 12
19 28
20 18
21 35
22 42
23 64
24 20
25 44
26 37
27 71
28 49
29 76
30 81
31 122
32 6
33 15
34 19
33 38
36 23
37 43
38 41
39 73
40 27
41 47
42 54
43 78
44 57
45 86
46 90
47 126
48 32
49 51
50 61
51 89
52 65
53 95
54 99
55 133
56 70
57 101
58 107
59 141
60 114
61 147
62 155
63 192
64 8
65 21
66 24
67 46
68 31
69 50
70 56
71 84
72 34
73 63
74 52
75 91
76 67
77 97
78 106
79 137
80 39
81 59
82 68
83 100
84 75
85 103
86 112
87 146
88 82
89 115
90 120
91 152
92 127
93 162
94 167
95 201
96 45
97 72
98 79
99 109
100 87
101 116
102 123
103 159
104 92
105 124
106 132
107 166
108 140
109 170
110 177
111 207
112 102
113 135
114 142
115 173
116 148
117 179
118 184
119 212
120 158
121 186
122 191
123 217
124 196
125 220
126 227
127 243
128 13
129 25
130 36
131 58
132 29
133 66
134 62
135 104
136 40
137 69
138 74
139 110
140 80
141 118
142 119
143 156
144 48
145 77
146 83
147 117
148 88
149 125
150 131
151 163
152 98
153 130
154 136
155 169
156 145
157 175
158 182
159 211
160 53
161 85
162 96
163 129
164 93
165 134
166 139
167 174
168 108
169 144
170 149
171 180
172 157
173 185
174 190
175 216
176 113
177 151
178 160
179 188
180 165
181 195
182 199
183 222
184 172
185 202
186 204
187 224
188 209
189 231
190 234
191 247
192 55
193 94
194 105
195 143
196 111
197 150
198 154
199 187
200 121
201 153
202 161
203 194
204 168
205 197
206 203
207 225
208 128
209 164
210 171
211 200
212 178
213 205
214 208
215 229
216 183
217 210
218 214
219 232
220 219
221 236
222 238
223 249
224 138
225 176
226 181
227 206
228 189
229 213
230 215
231 235
232 193
233 218
234 221
235 237
236 226
237 239
238 241
239 250
240 198
241 223
242 228
243 240
244 230
245 242
246 244
247 251
248 233
249 245
250 246
251 252
252 248
253 253
254 254
255 255
Sequence Z4, having a sequence length of 128:
[0, 1, 4, 9, 2, 11, 7, 21, 3, 13, 16, 24, 10, 27, 30, 51, 5, 15, 12, 26, 17, 32, 37, 54, 19, 39, 33, 59, 43, 63, 66, 90, 6, 14, 18, 34, 22, 38, 36, 61, 25, 42, 47, 64, 49, 69, 72, 93, 29, 45, 52, 71, 55, 75, 77, 96, 58, 79, 83, 100, 86, 103, 106, 119, 8, 20, 23, 41, 28, 44, 48, 68, 31, 53, 46, 73, 56, 76, 82, 98, 35, 50, 57, 78, 62, 81, 85, 102, 67, 87, 89, 105, 94, 109, 111, 121, 40, 60, 65, 84, 70, 88, 91, 108, 74, 92, 95, 110, 99, 112, 114, 122, 80, 97, 101, 113, 104, 115, 116, 123, 107, 117, 118, 124, 120, 125, 126, 127]
TABLE Z4
having a sequence length of 128:
Polarized channel Reliability or sequence
sequence number number of reliability
0 0
1 1
2 4
3 9
4 2
5 11
6 7
7 21
8 3
9 13
10 16
11 24
12 10
13 27
14 30
15 51
16 5
17 15
18 12
19 26
20 17
21 32
22 37
23 54
24 19
25 39
26 33
27 59
28 43
29 63
30 66
31 90
32 6
33 14
34 18
35 34
36 22
37 38
38 36
39 61
40 25
41 42
42 47
43 64
44 49
45 69
46 72
47 93
48 29
49 45
50 52
51 71
52 55
53 75
54 77
55 96
56 58
57 79
58 83
59 100
60 86
61 103
62 106
63 119
64 8
65 20
66 23
67 41
68 28
69 44
70 48
71 68
72 31
73 53
74 46
75 73
76 56
77 76
78 82
79 98
80 35
81 50
82 57
83 78
84 62
85 81
86 85
87 102
88 67
89 87
90 89
91 105
92 94
93 109
94 111
95 121
96 40
97 60
98 65
99 84
100 70
101 88
102 91
103 108
104 74
105 92
106 95
107 110
108 99
109 112
110 114
111 122
112 80
113 97
114 101
115 113
116 104
117 115
118 116
119 123
120 107
121 117
122 118
123 124
124 120
125 125
126 126
127 127
Sequence Z5, having a sequence length of 64:
[0, 1, 4, 8, 2, 10, 7, 19, 3, 12, 15, 21, 9, 24, 26, 39, 5, 14, 11, 23, 16, 27, 31, 41, 18, 33, 28, 44, 35, 46, 48, 57, 6, 13, 17, 29, 20, 32, 30, 45, 22, 34, 37, 47, 38, 49, 51, 58, 25, 36, 40, 50, 42, 52, 53, 59, 43, 54, 55, 60, 56, 61, 62, 63]
TABLE Z5
having a sequence length of 64:
Polarized channel Reliability or sequence
sequence number number of reliability
0 0
1 1
2 4
3 8
4 2
5 10
6 7
7 19
8 3
9 12
10 15
11 21
12 9
13 24
14 26
15 39
16 5
17 14
18 11
19 23
20 16
21 27
22 31
23 41
24 18
25 33
26 28
27 44
28 35
29 46
30 48
31 57
32 6
33 13
34 17
35 29
36 20
37 32
38 30
39 45
40 22
41 34
42 37
43 47
44 38
45 49
46 51
47 58
48 25
49 36
50 40
51 50
52 42
53 52
54 53
55 59
56 43
57 54
58 55
59 60
60 56
61 61
62 62
63 63
Second group of sequences (obtained by using a criterion that comprehensively considers performance obtained by List (list) whose sizes are respectively 1, 2, 4, 8, and 16, and preferentially considers performance of Lists 1 and 16).
Sequence Q6, having a sequence length of 1024:
[0, 1, 2, 4, 8, 16, 32, 3, 5, 64, 9, 6, 17, 10, 18, 128, 12, 33, 256, 36, 24, 20, 65, 34, 7, 129, 66, 512, 11, 40, 68, 13, 19, 130, 48, 14, 72, 257, 21, 132, 35, 258, 26, 513, 80, 37, 25, 22, 136, 38, 260, 96, 514, 264, 67, 41, 144, 28, 69, 42, 516, 49, 74, 272, 160, 520, 288, 528, 70, 131, 544, 192, 44, 81, 50, 73, 133, 15, 52, 320, 23, 134, 76, 82, 56, 384, 137, 97, 27, 39, 259, 84, 138, 145, 261, 29, 43, 98, 515, 88, 140, 30, 146, 71, 262, 265, 161, 576, 45, 100, 640, 51, 148, 46, 75, 266, 273, 517, 104, 162, 53, 193, 152, 77, 164, 768, 268, 274, 518, 54, 83, 57, 521, 112, 135, 78, 289, 194, 85, 276, 522, 58, 168, 139, 99, 86, 60, 280, 89, 290, 529, 524, 196, 141, 101, 147, 176, 142, 530, 31, 292, 200, 263, 90, 149, 321, 322, 102, 545, 105, 532, 92, 47, 296, 163, 150, 546, 208, 385, 267, 304, 324, 153, 165, 536, 386, 106, 55, 328, 577, 548, 113, 154, 79, 224, 108, 269, 166, 578, 519, 552, 195, 270, 641, 523, 580, 560, 275, 59, 169, 156, 291, 277, 114, 87, 197, 116, 170, 61, 531, 525, 642, 281, 278, 526, 177, 293, 388, 91, 584, 769, 198, 172, 120, 201, 336, 62, 282, 143, 103, 178, 294, 93, 644, 202, 592, 323, 392, 297, 151, 209, 284, 180, 107, 94, 204, 770, 648, 298, 352, 533, 325, 608, 155, 210, 400, 305, 547, 300, 109, 184, 534, 772, 326, 656, 115, 167, 157, 537, 225, 306, 329, 110, 117, 212, 171, 330, 226, 549, 776, 538, 387, 308, 216, 416, 672, 337, 158, 271, 118, 279, 550, 332, 579, 540, 389, 173, 121, 553, 199, 784, 179, 228, 338, 312, 704, 390, 122, 554, 581, 393, 283, 174, 203, 340, 448, 561, 353, 394, 181, 527, 582, 556, 63, 295, 285, 232, 124, 643, 585, 562, 205, 182, 286, 299, 354, 211, 401, 185, 396, 344, 586, 645, 593, 535, 240, 206, 95, 327, 564, 800, 402, 356, 307, 301, 417, 186, 404, 213, 418, 539, 568, 594, 649, 771, 227, 832, 588, 646, 302, 111, 360, 214, 551, 609, 896, 188, 309, 449, 331, 217, 408, 229, 541, 159, 420, 596, 650, 773, 310, 333, 119, 339, 218, 368, 657, 230, 391, 542, 610, 233, 313, 334, 774, 658, 612, 175, 123, 314, 555, 600, 583, 341, 450, 652, 220, 557, 424, 395, 777, 673, 355, 287, 183, 234, 125, 241, 563, 660, 558, 616, 778, 674, 316, 342, 345, 397, 452, 432, 207, 785, 403, 357, 187, 587, 565, 664, 624, 780, 236, 126, 242, 398, 705, 346, 456, 358, 405, 303, 569, 595, 244, 786, 189, 676, 589, 566, 647, 361, 706, 215, 348, 419, 406, 464, 801, 590, 409, 680, 788, 362, 570, 597, 572, 311, 708, 219, 598, 601, 651, 611, 410, 802, 421, 792, 231, 602, 653, 248, 688, 369, 190, 480, 335, 364, 613, 659, 654, 422, 315, 221, 370, 425, 235, 451, 412, 343, 372, 317, 614, 775, 222, 543, 426, 453, 237, 559, 833, 804, 712, 834, 661, 808, 779, 617, 604, 433, 720, 816, 836, 347, 897, 243, 662, 454, 318, 675, 376, 567, 618, 665, 736, 898, 840, 781, 428, 625, 238, 359, 458, 399, 245, 434, 677, 457, 591, 349, 127, 666, 787, 678, 620, 782, 626, 571, 191, 407, 350, 436, 465, 246, 460, 363, 681, 599, 249, 411, 668, 707, 573, 789, 803, 790, 682, 365, 440, 628, 709, 374, 423, 466, 250, 371, 689, 793, 481, 413, 603, 574, 366, 468, 655, 900, 805, 429, 615, 710, 252, 373, 848, 684, 713, 605, 690, 632, 482, 794, 806, 427, 414, 663, 835, 904, 809, 714, 619, 796, 472, 223, 455, 692, 721, 837, 716, 864, 810, 606, 912, 722, 696, 377, 817, 435, 812, 319, 484, 430, 621, 838, 667, 239, 461, 378, 459, 627, 622, 437, 488, 380, 818, 496, 669, 679, 724, 841, 629, 351, 467, 438, 737, 251, 462, 442, 441, 469, 247, 683, 842, 738, 899, 670, 783, 849, 820, 728, 928, 791, 367, 901, 630, 685, 844, 633, 711, 253, 691, 824, 902, 686, 740, 850, 375, 444, 470, 483, 415, 485, 905, 795, 473, 634, 744, 852, 960, 865, 693, 797, 906, 715, 807, 474, 636, 694, 254, 717, 575, 811, 697, 866, 798, 379, 431, 913, 607, 489, 723, 486, 908, 718, 813, 476, 856, 839, 725, 698, 914, 752, 868, 819, 814, 439, 929, 490, 623, 671, 739, 916, 872, 381, 930, 497, 821, 463, 726, 961, 843, 492, 631, 729, 700, 443, 741, 845, 920, 382, 822, 851, 730, 498, 880, 742, 445, 903, 687, 825, 932, 471, 635, 846, 500, 745, 962, 826, 732, 446, 936, 255, 853, 475, 753, 695, 867, 637, 907, 487, 746, 828, 854, 504, 799, 909, 857, 964, 719, 477, 915, 699, 493, 748, 944, 858, 873, 638, 968, 478, 383, 754, 869, 491, 910, 815, 917, 727, 870, 701, 931, 499, 860, 756, 922, 731, 976, 918, 874, 823, 502, 933, 743, 760, 881, 494, 702, 921, 827, 876, 501, 847, 992, 934, 447, 733, 882, 937, 963, 747, 505, 855, 924, 734, 829, 965, 884, 938, 506, 749, 945, 966, 755, 859, 940, 830, 911, 871, 639, 888, 479, 946, 750, 969, 508, 861, 757, 970, 919, 875, 862, 758, 948, 977, 923, 972, 761, 877, 952, 495, 703, 935, 978, 883, 762, 503, 925, 878, 735, 993, 885, 939, 994, 980, 926, 764, 941, 967, 886, 831, 947, 507, 889, 984, 751, 942, 996, 971, 890, 509, 949, 973, 1000, 892, 950, 863, 759, 1008, 510, 979, 953, 763, 974, 954, 879, 981, 982, 927, 995, 765, 956, 887, 985, 997, 986, 943, 891, 998, 766, 511, 988, 1001, 951, 1002, 893, 975, 894, 1009, 955, 1004, 1010, 957, 983, 958, 987, 1012, 999, 1016, 767, 989, 1003, 990, 1005, 959, 1011, 1013, 895, 1006, 1014, 1017, 1018, 991, 1020, 1007, 1015, 1019, 1021, 1022, 1023]
TABLE Q6
having a sequence length of 1024:
Reliability or sequence Polarized channel
number of reliability sequence number
0 0
1 1
2 2
3 4
4 8
5 16
6 32
7 3
8 5
9 64
10 9
11 6
12 17
13 10
14 18
15 128
16 12
17 33
18 256
19 36
20 24
21 20
22 65
23 34
24 7
25 129
26 66
27 512
28 11
29 40
30 68
31 13
32 19
33 130
34 48
35 14
36 72
37 257
38 21
39 132
40 35
41 258
42 26
43 513
44 80
45 37
46 25
47 22
48 136
49 38
50 260
51 96
52 514
53 264
54 67
55 41
56 144
57 28
58 69
59 42
60 516
61 49
62 74
63 272
64 160
65 520
66 288
67 528
68 70
69 131
70 544
71 192
72 44
73 81
74 50
75 73
76 133
77 15
78 52
79 320
80 23
81 134
82 76
83 82
84 56
85 384
86 137
87 97
88 27
89 39
90 259
91 84
92 138
93 145
94 261
95 29
96 43
97 98
98 515
99 88
100 140
101 30
102 146
103 71
104 262
105 265
106 161
107 576
108 45
109 100
110 640
111 51
112 148
113 46
114 75
115 266
116 273
117 517
118 104
119 162
120 53
121 193
122 152
123 77
124 164
125 768
126 268
127 274
128 518
129 54
130 83
131 57
132 521
133 112
134 135
135 78
136 289
137 194
138 85
139 276
140 522
141 58
142 168
143 139
144 99
145 86
146 60
147 280
148 89
149 290
150 529
151 524
152 196
153 141
154 101
155 147
156 176
157 142
158 530
159 31
160 292
161 200
162 263
163 90
164 149
165 321
166 322
167 102
168 545
169 105
170 532
171 92
172 47
173 296
174 163
175 150
176 546
177 208
178 385
179 267
180 304
181 324
182 153
183 165
184 536
185 386
186 106
187 55
188 328
189 577
190 548
191 113
192 154
193 79
194 224
195 108
196 269
197 166
198 578
199 519
200 552
201 195
202 270
203 641
204 523
205 580
206 560
207 275
208 59
209 169
210 156
211 291
212 277
213 114
214 87
215 197
216 116
217 170
218 61
219 531
220 525
221 642
222 281
223 278
224 526
225 177
226 293
227 388
228 91
229 584
230 769
231 198
232 172
233 120
234 201
235 336
236 62
237 282
238 143
239 103
240 178
241 294
242 93
243 644
244 202
245 592
246 323
247 392
248 297
249 151
250 209
251 284
252 180
253 107
254 94
255 204
256 770
257 648
258 298
259 352
260 533
261 325
262 608
263 155
264 210
265 400
266 305
267 547
268 300
269 109
270 184
271 534
272 772
273 326
274 656
275 115
276 167
277 157
278 537
279 225
280 306
281 329
282 110
283 117
284 212
285 171
286 330
287 226
288 549
289 776
290 538
291 387
292 308
293 216
294 416
295 672
296 337
297 158
298 271
299 118
300 279
301 550
302 332
303 579
304 540
305 389
306 173
307 121
308 553
309 199
310 784
311 179
312 228
313 338
314 312
315 704
316 390
317 122
318 554
319 581
320 393
321 283
322 174
323 203
324 340
325 448
326 561
327 353
328 394
329 181
330 527
331 582
332 556
333 63
334 295
335 285
336 232
337 124
338 643
339 585
340 562
341 205
342 182
343 286
344 299
345 354
346 211
347 401
348 185
349 3%
350 344
351 586
352 645
353 593
354 535
355 240
356 206
357 95
358 327
359 564
360 800
361 402
362 356
363 307
364 301
365 417
366 186
367 404
368 213
369 418
370 539
371 568
372 594
373 649
374 771
375 227
376 832
377 588
378 646
379 302
380 111
381 360
382 214
383 551
384 609
385 896
386 188
387 309
388 449
389 331
390 217
391 408
392 229
393 541
394 159
395 420
396 5%
397 650
398 773
399 310
400 333
401 119
402 339
403 218
404 368
405 657
406 230
407 391
408 542
409 610
410 233
411 313
412 334
413 774
414 658
415 612
416 175
417 123
418 314
419 555
420 600
421 583
422 341
423 450
424 652
425 220
426 557
427 424
428 395
429 777
430 673
431 355
432 287
433 183
434 234
435 125
436 241
437 563
438 660
439 558
440 616
441 778
442 674
443 316
444 342
445 345
446 397
447 452
448 432
449 207
450 785
451 403
452 357
453 187
454 587
455 565
456 664
457 624
458 780
459 236
460 126
461 242
462 398
463 705
464 346
465 456
466 358
467 405
468 303
469 569
470 595
471 244
472 786
473 189
474 676
475 589
476 566
477 647
478 361
479 706
480 215
481 348
482 419
483 406
484 464
485 801
486 590
487 409
488 680
489 788
490 362
491 570
492 597
493 572
494 311
495 708
496 219
497 598
498 601
499 651
500 611
501 410
502 802
503 421
504 792
505 231
506 602
507 653
508 248
509 688
510 369
511 190
512 480
513 335
514 364
515 613
516 659
517 654
518 422
519 315
520 221
521 370
522 425
523 235
524 451
525 412
526 343
527 372
528 317
529 614
530 775
531 222
532 543
533 426
534 453
535 237
536 559
537 833
538 804
539 712
540 834
541 661
542 808
543 779
544 617
545 604
546 433
547 720
548 816
549 836
550 347
551 897
552 243
553 662
554 454
555 318
556 675
557 376
558 567
559 618
560 665
561 736
562 898
563 840
564 781
565 428
566 625
567 238
568 359
569 458
570 399
571 245
572 434
573 677
574 457
575 591
576 349
577 127
578 666
579 787
580 678
581 620
582 782
583 626
584 571
585 191
586 407
587 350
588 436
589 465
590 246
591 460
592 363
593 681
594 599
595 249
596 411
597 668
598 707
599 573
600 789
601 803
602 790
603 682
604 365
605 440
606 628
607 709
608 374
609 423
610 466
611 250
612 371
613 689
614 793
615 481
616 413
617 603
618 574
619 366
620 468
621 655
622 900
623 805
624 429
625 615
626 710
627 252
628 373
629 848
630 684
631 713
632 605
633 690
634 632
635 482
636 794
637 806
638 427
639 414
640 663
641 835
642 904
643 809
644 714
645 619
646 796
647 472
648 223
649 455
650 692
651 721
652 837
653 716
654 864
655 810
656 606
657 912
658 722
659 696
660 377
661 817
662 435
663 812
664 319
665 484
666 430
667 621
668 838
669 667
670 239
671 461
672 378
673 459
674 627
675 622
676 437
677 488
678 380
679 818
680 496
681 669
682 679
683 724
684 841
685 629
686 351
687 467
688 438
689 737
690 251
691 462
692 442
693 441
694 469
695 247
696 683
697 842
698 738
699 899
700 670
701 783
702 849
703 820
704 728
705 928
706 791
707 367
708 901
709 630
710 685
711 844
712 633
713 711
714 253
715 691
716 824
717 902
718 686
719 740
720 850
721 375
722 444
723 470
724 483
725 415
726 485
727 905
728 795
729 473
730 634
731 744
732 852
733 960
734 865
735 693
736 797
737 906
738 715
739 807
740 474
741 636
742 694
743 254
744 717
745 575
746 811
747 697
748 866
749 798
750 379
751 431
752 913
753 607
754 489
755 723
756 486
757 908
758 718
759 813
760 476
761 856
762 839
763 725
764 698
765 914
766 752
767 868
768 819
769 814
770 439
771 929
772 490
773 623
774 671
775 739
776 916
777 872
778 381
779 930
780 497
781 821
782 463
783 726
784 961
785 843
786 492
787 631
788 729
789 700
790 443
791 741
792 845
793 920
794 382
795 822
796 851
797 730
798 498
799 880
800 742
801 445
802 903
803 687
804 825
805 932
806 471
807 635
808 846
809 500
810 745
811 962
812 826
813 732
814 446
815 936
816 255
817 853
818 475
819 753
820 695
821 867
822 637
823 907
824 487
825 746
826 828
827 854
828 504
829 799
830 909
831 857
832 964
833 719
834 477
835 915
836 699
837 493
838 748
839 944
840 858
841 873
842 638
843 968
844 478
845 383
846 754
847 869
848 491
849 910
850 815
851 917
852 727
853 870
854 701
855 931
856 499
857 860
858 756
859 922
860 731
861 976
862 918
863 874
864 823
865 502
866 933
867 743
868 760
869 881
870 494
871 702
872 921
873 827
874 876
875 501
876 847
877 992
878 934
879 447
880 733
881 882
882 937
883 963
884 747
885 505
886 855
887 924
888 734
889 829
890 965
891 884
892 938
893 506
894 749
895 945
896 966
897 755
898 859
899 940
900 830
901 911
902 871
903 639
904 888
905 479
906 946
907 750
908 969
909 508
910 861
911 757
912 970
913 919
914 875
915 862
916 758
917 948
918 977
919 923
920 972
921 761
922 877
923 952
924 495
925 703
926 935
927 978
928 883
929 762
930 503
931 925
932 878
933 735
934 993
935 885
936 939
937 994
938 980
939 926
940 764
941 941
942 967
943 886
944 831
945 947
946 507
947 889
948 984
949 751
950 942
951 996
952 971
953 890
954 509
955 949
956 973
957 1000
958 892
959 950
960 863
961 759
962 1008
963 510
964 979
965 953
966 763
967 974
968 954
969 879
970 981
971 982
972 927
973 995
974 765
975 956
976 887
977 985
978 997
979 986
980 943
981 891
982 998
983 766
984 511
985 988
986 1001
987 951
988 1002
989 893
990 975
991 894
992 1009
993 955
994 1004
995 1010
996 957
997 983
998 958
999 987
1000 1012
1001 999
1002 1016
1003 767
1004 989
1005 1003
1006 990
1007 1005
1008 959
1009 1011
1010 1013
1011 895
1012 1006
1013 1014
1014 1017
1015 1018
1016 991
1017 1020
1018 1007
1019 1015
1020 1019
1021 1021
1022 1022
1023 1023
Sequence Q7, having a sequence length of 512:
[0, 1, 2, 4, 8, 16, 32, 3, 5, 64, 9, 6, 17, 10, 18, 128, 12, 33, 256, 36, 24, 20, 65, 34, 7, 129, 66, 11, 40, 68, 13, 19, 130, 48, 14, 72, 257, 21, 132, 35, 258, 26, 80, 37, 25, 22, 136, 38, 260, 96, 264, 67, 41, 144, 28, 69, 42, 49, 74, 272, 160, 288, 70, 131, 192, 44, 81, 50, 73, 133, 15, 52, 320, 23, 134, 76, 82, 56, 384, 137, 97, 27, 39, 259, 84, 138, 145, 261, 29, 43, 98, 88, 140, 30, 146, 71, 262, 265, 161, 45, 100, 51, 148, 46, 75, 266, 273, 104, 162, 53, 193, 152, 77, 164, 268, 274, 54, 83, 57, 112, 135, 78, 289, 194, 85, 276, 58, 168, 139, 99, 86, 60, 280, 89, 290, 196, 141, 101, 147, 176, 142, 31, 292, 200, 263, 90, 149, 321, 322, 102, 105, 92, 47, 296, 163, 150, 208, 385, 267, 304, 324, 153, 165, 386, 106, 55, 328, 113, 154, 79, 224, 108, 269, 166, 195, 270, 275, 59, 169, 156, 291, 277, 114, 87, 197, 116, 170, 61, 281, 278, 177, 293, 388, 91, 198, 172, 120, 201, 336, 62, 282, 143, 103, 178, 294, 93, 202, 323, 392, 297, 151, 209, 284, 180, 107, 94, 204, 298, 352, 325, 155, 210, 400, 305, 300, 109, 184, 326, 115, 167, 157, 225, 306, 329, 110, 117, 212, 171, 330, 226, 387, 308, 216, 416, 337, 158, 271, 118, 279, 332, 389, 173, 121, 199, 179, 228, 338, 312, 390, 122, 393, 283, 174, 203, 340, 448, 353, 394, 181, 63, 295, 285, 232, 124, 205, 182, 286, 299, 354, 211, 401, 185, 396, 344, 240, 206, 95, 327, 402, 356, 307, 301, 417, 186, 404, 213, 418, 227, 302, 111, 360, 214, 188, 309, 449, 331, 217, 408, 229, 159, 420, 310, 333, 119, 339, 218, 368, 230, 391, 233, 313, 334, 175, 123, 314, 341, 450, 220, 424, 395, 355, 287, 183, 234, 125, 241, 316, 342, 345, 397, 452, 432, 207, 403, 357, 187, 236, 126, 242, 398, 346, 456, 358, 405, 303, 244, 189, 361, 215, 348, 419, 406, 464, 409, 362, 311, 219, 410, 421, 231, 248, 369, 190, 480, 335, 364, 422, 315, 221, 370, 425, 235, 451, 412, 343, 372, 317, 222, 426, 453, 237, 433, 347, 243, 454, 318, 376, 428, 238, 359, 458, 399, 245, 434, 457, 349, 127, 191, 407, 350, 436, 465, 246, 460, 363, 249, 411, 365, 440, 374, 423, 466, 250, 371, 481, 413, 366, 468, 429, 252, 373, 482, 427, 414, 472, 223, 455, 377, 435, 319, 484, 430, 239, 461, 378, 459, 437, 488, 380, 496, 351, 467, 438, 251, 462, 442, 441, 469, 247, 367, 253, 375, 444, 470, 483, 415, 485, 473, 474, 254, 379, 431, 489, 486, 476, 439, 490, 381, 497, 463, 492, 443, 382, 498, 445, 471, 500, 446, 255, 475, 487, 504, 477, 493, 478, 383, 491, 499, 502, 494, 501, 447, 505, 506, 479, 508, 495, 503, 507, 509, 510, 511]
TABLE Q7
having a sequence length of 512:
Relia- Relia- Relia- Relia- Relia- Relia- Relia- Relia-
bility Polar- bility Polar- bility Polar- bility Polar- bility Polar- bility Polar- bility Polar- bility Polar-
or ized or ized or ized or ized or ized or ized or ized or ized
se- chan- se- chan- se- chan- se- chan- se- chan- se- chan- se- chan- se- chan-
quence nel quence nel quence nel quence nel quence nel quence nel quence nel quence nel
num- se- num- se- num- se- num- se- num- se- num- se- num- se- num- se-
ber quen- ber quen- ber quen- ber quen- ber quen- ber quen- ber quen- ber quen-
of ce of ce of ce of ce of ce of ce of ce of ce
relia- num- relia- num- relia- num- relia- num- relia- num- relia- num- relia- num- relia- num-
bility ber bility ber bility ber bility ber bility ber bility ber bility ber bility ber
0 0 64 192 128 139 192 388 256 338 320 313 384 343 448 380
1 1 65 44 129 99 193 91 257 312 321 334 385 372 449 496
2 2 66 81 130 86 194 198 258 390 322 175 386 317 450 351
3 4 67 50 131 60 195 172 259 122 323 123 387 222 451 467
4 8 68 73 132 280 196 120 260 393 324 314 388 426 452 438
5 16 69 133 133 89 197 201 261 283 325 341 389 453 453 251
6 32 70 15 134 290 198 336 262 174 326 450 390 237 454 462
7 3 71 52 135 196 199 62 263 203 327 220 391 433 455 442
8 5 72 320 136 141 200 282 264 340 328 424 392 347 456 441
9 64 73 23 137 101 201 143 265 448 329 395 393 243 457 469
10 9 74 134 138 147 202 103 266 353 330 355 394 454 458 247
11 6 75 76 139 176 203 178 267 394 331 287 395 318 459 367
12 17 76 82 140 142 204 294 268 181 332 183 396 376 460 253
13 10 77 56 141 31 205 93 269 63 333 234 397 428 461 375
14 18 78 384 142 292 206 202 270 295 334 125 398 238 462 444
15 128 79 137 143 200 207 323 271 285 335 241 399 359 463 470
16 12 80 97 144 263 208 392 272 232 336 316 400 458 464 483
17 33 81 27 145 90 209 297 273 124 337 342 401 399 465 415
18 256 82 39 146 149 210 151 274 205 338 345 402 245 466 485
19 36 83 259 147 321 211 209 275 182 339 397 403 434 467 473
20 24 84 84 148 322 212 284 276 286 340 452 404 457 468 474
21 20 85 138 149 102 213 180 277 299 341 432 405 349 469 254
22 65 86 145 150 105 214 107 278 354 342 207 406 127 470 379
23 34 87 261 151 92 215 94 279 211 343 403 407 191 471 431
24 7 88 29 152 47 216 204 280 401 344 357 408 407 472 489
25 129 89 43 153 296 217 298 281 185 345 187 409 350 473 486
26 66 90 98 154 163 218 352 282 396 346 236 410 436 474 476
27 11 91 88 155 150 219 325 283 344 347 126 411 465 475 439
28 40 92 140 156 208 220 155 284 240 348 242 412 246 476 490
29 68 93 30 157 385 221 210 285 206 349 398 413 460 477 381
30 13 94 146 158 267 222 400 286 95 350 346 414 363 478 497
31 19 95 71 159 304 223 305 287 327 351 456 415 249 479 463
32 130 96 262 160 324 224 300 288 402 352 358 416 411 480 492
33 48 97 265 161 153 225 109 289 356 353 405 417 365 481 443
34 14 98 161 162 165 226 184 290 307 354 303 418 440 482 382
35 72 99 45 163 386 227 326 291 301 355 244 419 374 483 498
36 257 100 100 164 106 228 115 292 417 356 189 420 423 484 445
37 21 101 51 165 55 229 167 293 186 357 361 421 466 485 471
38 132 102 148 166 328 230 157 294 404 358 215 422 250 486 500
39 35 103 46 167 113 231 225 295 213 359 348 423 371 487 446
40 258 104 75 168 154 232 306 296 418 360 419 424 481 488 255
41 26 105 266 169 79 233 329 297 227 361 406 425 413 489 475
42 80 106 273 170 224 234 110 298 302 362 464 426 366 490 487
43 37 107 104 171 108 235 117 299 111 363 409 427 468 491 504
44 25 108 162 172 269 236 212 300 360 364 362 428 429 492 477
45 22 109 53 173 166 237 171 301 214 365 311 429 252 493 493
46 136 110 193 174 195 238 330 302 188 366 219 430 373 494 478
47 38 111 152 175 270 239 226 303 309 367 410 431 482 495 383
48 260 112 77 176 275 240 387 304 449 368 421 432 427 496 491
49 96 113 164 177 59 241 308 305 331 369 231 433 414 497 499
50 264 114 268 178 169 242 216 306 217 370 248 434 472 498 502
51 67 115 274 179 156 243 416 307 408 371 369 435 223 499 494
52 41 116 54 180 291 244 337 308 229 372 190 436 455 500 501
53 144 117 83 181 277 245 158 309 159 373 480 437 377 501 447
54 28 118 57 182 114 246 271 310 420 374 335 438 435 502 505
55 69 119 112 183 87 247 118 311 310 375 364 439 319 503 506
56 42 120 135 184 197 248 279 312 333 376 422 440 484 504 479
57 49 121 78 185 116 249 332 313 119 377 315 441 430 505 508
58 74 122 289 186 170 250 389 314 339 378 221 442 239 506 495
59 272 123 194 187 61 251 173 315 218 379 370 443 461 507 503
60 160 124 85 188 281 252 121 316 368 380 425 444 378 508 507
61 288 125 276 189 278 253 199 317 230 381 235 445 459 509 509
62 70 126 58 190 177 254 179 318 391 382 451 446 437 510 510
63 131 127 168 191 293 255 228 319 233 383 412 447 488 511 511
Sequence Q8, having a sequence length of 256:
[0, 1, 2, 4, 8, 16, 32, 3, 5, 64, 9, 6, 17, 10, 18, 128, 12, 33, 36, 24, 20, 65, 34, 7, 129, 66, 11, 40, 68, 13, 19, 130, 48, 14, 72, 21, 132, 35, 26, 80, 37, 25, 22, 136, 38, 96, 67, 41, 144, 28, 69, 42, 49, 74, 160, 70, 131, 192, 44, 81, 50, 73, 133, 15, 52, 23, 134, 76, 82, 56, 137, 97, 27, 39, 84, 138, 145, 29, 43, 98, 88, 140, 30, 146, 71, 161, 45, 100, 51, 148, 46, 75, 104, 162, 53, 193, 152, 77, 164, 54, 83, 57, 112, 135, 78, 194, 85, 58, 168, 139, 99, 86, 60, 89, 196, 141, 101, 147, 176, 142, 31, 200, 90, 149, 102, 105, 92, 47, 163, 150, 208, 153, 165, 106, 55, 113, 154, 79, 224, 108, 166, 195, 59, 169, 156, 114, 87, 197, 116, 170, 61, 177, 91, 198, 172, 120, 201, 62, 143, 103, 178, 93, 202, 151, 209, 180, 107, 94, 204, 155, 210, 109, 184, 115, 167, 157, 225, 110, 117, 212, 171, 226, 216, 158, 118, 173, 121, 199, 179, 228, 122, 174, 203, 181, 63, 232, 124, 205, 182, 211, 185, 240, 206, 95, 186, 213, 227, 111, 214, 188, 217, 229, 159, 119, 218, 230, 233, 175, 123, 220, 183, 234, 125, 241, 207, 187, 236, 126, 242, 244, 189, 215, 219, 231, 248, 190, 221, 235, 222, 237, 243, 238, 245, 127, 191, 246, 249, 250, 252, 223, 239, 251, 247, 253, 254, 255]
TABLE Q8
having a sequence length of 256:
Relia- Relia- Relia- Relia- Relia- Relia- Relia- Relia-
bility Polar- bility Polar- bility Polar- bility Polar- bility Polar- bility Polar- bility Polar- bility Polar-
or ized or ized or ized or ized or ized or ized or ized or ized
se- chan- se- chan- se- chan- se- chan- se- chan- se- chan- se- chan- se- chan-
quence nel quence nel quence nel quence nel quence nel quence nel quence nel quence nel
num- se- num- se- num- se- num- se- num- se- num- se- num- se- num- se-
ber quen- ber quen- ber quen- ber quen- ber quen- ber quen- ber quen- ber quen-
of ce of ce of ce of ce of ce of ce of ce of ce
relia- num- relia- num- relia- num- relia- num- relia- num- relia- num- relia- num- relia- num-
bility ber bility ber bility ber bility ber bility ber bility ber bility ber bility ber
0 0 32 48 64 52 96 152 128 163 160 178 192 203 224 207
1 1 33 14 65 23 97 77 129 150 161 93 193 181 225 187
2 2 34 72 66 134 98 164 130 208 162 202 194 63 226 236
3 4 35 21 67 76 99 54 131 153 163 151 195 232 227 126
4 8 36 132 68 82 100 83 132 165 164 209 196 124 228 242
5 16 37 35 69 56 101 57 133 106 165 180 197 205 229 244
6 32 38 26 70 137 102 112 134 55 166 107 198 182 230 189
7 3 39 80 71 97 103 135 135 113 167 94 199 211 231 215
8 5 40 37 72 27 104 78 136 154 168 204 200 185 232 219
9 64 41 25 73 39 105 194 137 79 169 155 201 240 233 231
10 9 42 22 74 84 106 85 138 224 170 210 202 206 234 248
11 6 43 136 75 138 107 58 139 108 171 109 203 95 235 190
12 17 44 38 76 145 108 168 140 166 172 184 204 186 236 221
13 10 45 96 77 29 109 139 141 195 173 115 205 213 237 235
14 18 46 67 78 43 110 99 142 59 174 167 206 227 238 222
15 128 47 41 79 98 111 86 143 169 175 157 207 111 239 237
16 12 48 144 80 88 112 60 144 156 176 225 208 214 240 243
17 33 49 28 81 140 113 89 145 114 177 110 209 188 241 238
18 36 50 69 82 30 114 196 146 87 178 117 210 217 242 245
19 24 51 42 83 146 115 141 147 197 179 212 211 229 243 127
20 20 52 49 84 71 116 101 148 116 180 171 212 159 244 191
21 65 53 74 85 161 117 147 149 170 181 226 213 119 245 246
22 34 54 160 86 45 118 176 150 61 182 216 214 218 246 249
23 7 55 70 87 100 119 142 151 177 183 158 215 230 247 250
24 129 56 131 88 51 120 31 152 91 184 118 216 233 248 252
25 66 57 192 89 148 121 200 153 198 185 173 217 175 249 223
26 11 58 44 90 46 122 90 154 172 186 121 218 123 250 239
27 40 59 81 91 75 123 149 155 120 187 199 219 220 251 251
28 68 60 50 92 104 124 102 156 201 188 179 220 183 252 247
29 13 61 73 93 162 125 105 157 62 189 228 221 234 253 253
30 19 62 133 94 53 126 92 158 143 190 122 222 125 254 254
31 130 63 15 95 193 127 47 159 103 191 174 223 241 255 255
Sequence Q9, having a sequence length of 128:
[0, 1, 2, 4, 8, 16, 32, 3, 5, 64, 9, 6, 17, 10, 18, 12, 33, 36, 24, 20, 65, 34, 7, 66, 11, 40, 68, 13, 19, 48, 14, 72, 21, 35, 26, 80, 37, 25, 22, 38, 96, 67, 41, 28, 69, 42, 49, 74, 70, 44, 81, 50, 73, 15, 52, 23, 76, 82, 56, 97, 27, 39, 84, 29, 43, 98, 88, 30, 71, 45, 100, 51, 46, 75, 104, 53, 77, 54, 83, 57, 112, 78, 85, 58, 99, 86, 60, 89, 101, 31, 90, 102, 105, 92, 47, 106, 55, 113, 79, 108, 59, 114, 87, 116, 61, 91, 120, 62, 103, 93, 107, 94, 109, 115, 110, 117, 118, 121, 122, 63, 124, 95, 111, 119, 123, 125, 126, 127]
TABLE Q9
having a sequence length of 128:
Relia- Relia- Relia- Relia- Relia- Relia- Relia- Relia-
bility Polar- bility Polar- bility Polar- bility Polar- bility Polar- bility Polar- bility Polar- bility Polar-
or ized or ized or ized or ized or ized or ized or ized or ized
se- chan- se- chan- se- chan- se- chan- se- chan- se- chan- se- chan- se- chan-
quence nel quence nel quence nel quence nel quence nel quence nel quence nel quence nel
num- se- num- se- num- se- num- se- num- se- num- se- num- se- num- se-
ber quen- ber quen- ber quen- ber quen- ber quen- ber quen- ber quen- ber quen-
of ce of ce of ce of ce of ce of ce of ce of ce
relia- num- relia- num- relia- num- relia- num- relia- num- relia- num- relia- num- relia- num-
bility ber bility ber bility ber bility ber bility ber bility ber bility ber bility ber
0 0 16 33 32 21 48 70 64 43 80 112 96 55 112 109
1 1 17 36 33 35 49 44 65 98 81 78 97 113 113 115
2 2 18 24 34 26 50 81 66 88 82 85 98 79 114 110
3 4 19 20 35 80 51 50 67 30 83 58 99 108 115 117
4 8 20 65 36 37 52 73 68 71 84 99 100 59 116 118
5 16 21 34 37 25 53 15 69 45 85 86 101 114 117 121
6 32 22 7 38 22 54 52 70 100 86 60 102 87 118 122
7 3 23 66 39 38 55 23 71 51 87 89 103 116 119 63
8 5 24 11 40 96 56 76 72 46 88 101 104 61 120 124
9 64 25 40 41 67 57 82 73 75 89 31 105 91 121 95
10 9 26 68 42 41 58 56 74 104 90 90 106 120 122 111
11 6 27 13 43 28 59 97 75 53 91 102 107 62 123 119
12 17 28 19 44 69 60 27 76 77 92 105 108 103 124 123
13 10 29 48 45 42 61 39 77 54 93 92 109 93 125 125
14 18 30 14 46 49 62 84 78 83 94 47 110 107 126 126
15 12 31 72 47 74 63 29 79 57 95 106 111 94 127 127
Sequence Q10, having a sequence length of 64:
[0, 1, 2, 4, 8, 16, 32, 3, 5, 9, 6, 17, 10, 18, 12, 33, 36, 24, 20, 34, 7, 11, 40, 13, 19, 48, 14, 21, 35, 26, 37, 25, 22, 38, 41, 28, 42, 49, 44, 50, 15, 52, 23, 56, 27, 39, 29, 43, 30, 45, 51, 46, 53, 54, 57, 58, 60, 31, 47, 55, 59, 61, 62, 63]
TABLE Q10
having a sequence length of 64:
Relia- Relia- Relia- Relia- Relia- Relia- Relia- Relia-
bility Polar- bility Polar- bility Polar- bility Polar- bility Polar- bility Polar- bility Polar- bility Polar-
or ized or ized or ized or ized or ized or ized or ized or ized
se- chan- se- chan- se- chan- se- chan- se- chan- se- chan- se- chan- se- chan-
quence nel quence nel quence nel quence nel quence nel quence nel quence nel quence nel
num- se- num- se- num- se- num- se- num- se- num- se- num- se- num- se-
ber quen- ber quen- ber quen- ber quen- ber quen- ber quen- ber quen- ber quen-
of ce of ce of ce of ce of ce of ce of ce of ce
relia- num- relia- num- relia- num- relia- num- relia- num- relia- num- relia- num- relia- num-
bility ber bility ber bility ber bility ber bility ber bility ber bility ber bility ber
0 0 8 5 16 36 24 19 32 22 40 15 48 30 56 60
1 1 9 9 17 24 25 48 33 38 41 52 49 45 57 31
2 2 10 6 18 20 26 14 34 41 42 23 50 51 58 47
3 4 11 17 19 34 27 21 35 28 43 56 51 46 59 55
4 8 12 10 20 7 28 35 36 42 44 27 52 53 60 59
5 16 13 18 21 11 29 26 37 49 45 39 53 54 61 61
6 32 14 12 22 40 30 37 38 44 46 29 54 57 62 62
7 3 15 33 23 13 31 25 39 50 47 43 55 58 63 63
Sequence Z6, having a sequence length of 1024:
[0, 1, 2, 7, 3, 8, 11, 24, 4, 10, 13, 28, 16, 31, 35, 77, 5, 12, 14, 32, 21, 38, 47, 80, 20, 46, 42, 88, 57, 95, 101, 159, 6, 17, 23, 40, 19, 45, 49, 89, 29, 55, 59, 96, 72, 108, 113, 172, 34, 61, 74, 111, 78, 120, 129, 187, 84, 131, 141, 208, 146, 218, 236, 333, 9, 22, 26, 54, 30, 58, 68, 103, 36, 75, 62, 114, 82, 123, 135, 193, 44, 73, 83, 130, 91, 138, 145, 214, 99, 148, 163, 228, 171, 242, 254, 357, 51, 87, 97, 144, 109, 154, 167, 239, 118, 169, 186, 253, 195, 269, 282, 380, 133, 191, 213, 275, 216, 283, 299, 401, 233, 307, 317, 417, 337, 435, 460, 577, 15, 25, 33, 69, 39, 76, 81, 134, 48, 86, 92, 143, 100, 153, 157, 238, 56, 93, 102, 155, 112, 164, 175, 249, 122, 182, 192, 263, 210, 277, 297, 394, 64, 106, 119, 174, 124, 183, 197, 276, 142, 209, 217, 285, 232, 306, 322, 416, 156, 225, 240, 311, 252, 329, 342, 433, 270, 348, 366, 453, 386, 473, 511, 585, 71, 121, 137, 201, 152, 215, 231, 309, 161, 234, 244, 323, 255, 341, 356, 449, 177, 250, 264, 346, 284, 368, 382, 480, 293, 390, 403, 496, 425, 520, 531, 648, 194, 279, 287, 375, 312, 392, 406, 505, 336, 410, 434, 523, 459, 535, 567, 670, 355, 436, 461, 552, 471, 571, 590, 695, 508, 595, 611, 690, 627, 714, 743, 816, 18, 37, 41, 90, 50, 94, 104, 162, 53, 105, 115, 179, 126, 196, 202, 298, 63, 116, 127, 207, 139, 212, 223, 300, 147, 222, 237, 321, 251, 335, 343, 432, 66, 136, 149, 211, 160, 226, 241, 334, 173, 248, 258, 344, 268, 364, 379, 468, 180, 266, 280, 363, 292, 387, 399, 494, 314, 411, 418, 519, 443, 528, 555, 664, 79, 165, 166, 246, 181, 261, 273, 358, 188, 281, 286, 389, 302, 400, 412, 513, 235, 296, 313, 402, 324, 422, 444, 526, 350, 445, 464, 550, 481, 576, 587, 686, 259, 327, 345, 431, 362, 452, 466, 568, 381, 478, 490, 592, 514, 604, 619, 707, 404, 510, 521, 612, 527, 628, 608, 721, 557, 660, 672, 750, 678, 778, 794, 845, 85, 178, 185, 291, 227, 305, 316, 407, 247, 320, 328, 428, 349, 446, 462, 570, 265, 347, 361, 451, 367, 467, 483, 586, 391, 487, 501, 596, 525, 616, 639, 725, 294, 365, 369, 482, 395, 503, 518, 609, 427, 522, 533, 638, 565, 624, 666, 751, 448, 546, 572, 662, 588, 676, 688, 770, 605, 693, 692, 790, 722, 801, 814, 879, 325, 388, 423, 524, 447, 534, 554, 649, 465, 574, 569, 673, 591, 671, 691, 782, 484, 589, 610, 687, 620, 694, 723, 806, 647, 729, 740, 818, 760, 834, 844, 905, 512, 615, 635, 724, 665, 726, 756, 824, 677, 754, 772, 848, 786, 837, 870, 924, 680, 780, 798, 856, 809, 875, 865, 930, 828, 885, 893, 946, 909, 954, 963, 984, 27, 43, 52, 98, 60, 117, 128, 199, 65, 132, 140, 204, 151, 220, 224, 330, 67, 150, 158, 219, 170, 260, 271, 354, 184, 278, 290, 370, 304, 393, 408, 532, 70, 168, 176, 267, 190, 288, 301, 383, 200, 308, 318, 419, 332, 426, 439, 536, 206, 326, 340, 437, 359, 455, 476, 558, 371, 469, 491, 584, 493, 599, 618, 745, 107, 189, 198, 303, 205, 319, 331, 421, 229, 339, 351, 454, 377, 475, 486, 575, 245, 353, 372, 470, 396, 492, 497, 594, 420, 498, 506, 617, 545, 632, 656, 753, 262, 384, 409, 500, 415, 515, 529, 625, 440, 544, 559, 645, 581, 667, 675, 773, 457, 566, 583, 674, 606, 685, 709, 787, 634, 712, 730, 807, 741, 822, 842, 903, 110, 203, 221, 338, 243, 352, 378, 477, 257, 373, 397, 499, 424, 507, 517, 621, 274, 405, 414, 516, 438, 541, 553, 640, 456, 560, 578, 669, 597, 681, 700, 774, 295, 430, 442, 556, 474, 573, 580, 682, 488, 593, 603, 696, 630, 710, 718, 803, 509, 613, 633, 715, 650, 735, 742, 820, 659, 747, 764, 836, 789, 854, 871, 925, 315, 463, 479, 598, 495, 607, 626, 713, 539, 631, 644, 738, 653, 744, 758, 833, 547, 651, 658, 755, 683, 763, 783, 852, 704, 788, 797, 860, 813, 880, 888, 933, 561, 689, 698, 775, 719, 791, 800, 867, 731, 810, 825, 884, 838, 894, 907, 949, 766, 819, 846, 897, 858, 911, 916, 961, 868, 921, 929, 966, 940, 974, 983, 1003, 125, 230, 256, 374, 272, 398, 413, 530, 289, 429, 441, 543, 458, 564, 582, 701, 310, 450, 472, 579, 489, 600, 602, 706, 504, 614, 636, 728, 646, 736, 749, 829, 360, 485, 502, 601, 538, 623, 637, 739, 542, 643, 655, 746, 663, 759, 769, 850, 548, 661, 679, 768, 703, 781, 795, 864, 716, 804, 812, 873, 826, 889, 900, 944, 376, 537, 540, 641, 549, 652, 668, 762, 563, 684, 697, 785, 711, 792, 808, 876, 629, 702, 720, 796, 732, 817, 827, 886, 761, 831, 840, 898, 857, 910, 915, 960, 654, 734, 748, 821, 767, 847, 853, 902, 777, 841, 863, 914, 874, 922, 932, 969, 799, 869, 881, 928, 891, 935, 943, 976, 904, 947, 953, 981, 958, 989, 991, 1011, 385, 551, 562, 699, 622, 708, 717, 802, 642, 727, 737, 823, 757, 830, 849, 901, 657, 752, 765, 835, 776, 851, 862, 913, 793, 872, 859, 919, 887, 931, 939, 972, 705, 771, 779, 855, 805, 866, 878, 926, 815, 882, 892, 936, 899, 941, 950, 980, 839, 895, 906, 945, 917, 955, 959, 987, 923, 965, 968, 993, 975, 996, 998, 1008, 733, 784, 811, 883, 832, 890, 896, 942, 843, 908, 912, 952, 920, 956, 967, 990, 861, 918, 927, 964, 938, 970, 971, 997, 948, 977, 979, 999, 985, 1004, 1006, 1016, 877, 934, 937, 973, 951, 978, 982, 1001, 957, 986, 988, 1005, 994, 1007, 1012, 1018, 962, 992, 995, 1009, 1000, 1010, 1013, 1019, 1002, 1014, 1015, 1020, 1017, 1021, 1022, 1023]
TABLE Z6
having a sequence length of 1024:
Relia- Relia- Relia- Relia- Relia- Relia- Relia- Relia-
Polar- bility Polar- bility Polar- bility Polar- bility Polar- bility Polar- bility Polar- bility Polar- bility
ized or ized or ized or ized or ized or ized or ized or ized or
chan- se- chan- se- chan- se- chan- se- chan- se- chan- se- chan- se- chan- se-
nel quence nel quence nel quence nel quence nel quence nel quence nel quence nel quence
se- num- se- num- se- num- se- num- se- num- se- num- se- num- se- num-
quen- ber quen- ber quen- ber quen- ber quen- ber quen- ber quen- ber quen- ber
ce of ce of ce of ce of ce of ce of ce of ce of
num- relia- num- relia- num- relia- num- relia- num- relia- num- relia- num- relia- num- relia-
ber bility ber bility ber bility ber bility ber bility ber bility ber bility ber bility
0 0 128 15 256 18 384 85 512 27 640 110 768 125 896 385
1 1 129 25 257 37 385 178 513 43 641 203 769 230 897 551
2 2 130 33 258 41 386 185 514 52 642 221 770 256 898 562
3 7 131 69 259 90 387 291 515 98 643 338 771 374 899 699
4 3 132 39 260 50 388 227 516 60 644 243 772 272 900 622
5 8 133 76 261 94 389 305 517 117 645 352 773 398 901 708
6 11 134 81 262 104 390 316 518 128 646 378 774 413 902 717
7 24 135 134 263 162 391 407 519 199 647 477 775 530 903 802
8 4 136 48 264 53 392 247 520 65 648 257 776 289 904 642
9 10 137 86 265 105 393 320 521 132 649 373 777 429 905 727
10 13 138 92 266 115 394 328 522 140 650 397 778 441 906 737
11 28 139 143 267 179 395 428 523 204 651 499 779 543 907 823
12 16 140 100 268 126 396 349 524 151 652 424 780 458 908 757
13 31 141 153 269 196 397 446 525 220 653 507 781 564 909 830
14 35 142 157 270 202 398 462 526 224 654 517 782 582 910 849
15 77 143 238 271 298 399 570 527 330 655 621 783 701 911 901
16 5 144 56 272 63 400 265 528 67 656 274 784 310 912 657
17 12 145 93 273 116 401 347 529 150 657 405 785 450 913 752
18 14 146 102 274 127 402 361 530 158 658 414 786 472 914 765
19 32 147 155 275 207 403 451 531 219 659 516 787 579 915 835
20 21 148 112 276 139 404 367 532 170 660 438 788 489 916 776
21 38 149 164 277 212 405 467 533 260 661 541 789 600 917 851
22 47 150 175 278 223 406 483 534 271 662 553 790 602 918 862
23 80 151 249 279 300 407 586 535 354 663 640 791 706 919 913
24 20 152 122 280 147 408 391 536 184 664 456 792 504 920 793
25 46 153 182 281 222 409 487 537 278 665 560 793 614 921 872
26 42 154 192 282 237 410 501 538 290 666 578 794 636 922 859
27 88 155 263 283 321 411 596 539 370 667 669 795 728 923 919
28 57 156 210 284 251 412 525 540 304 668 597 796 646 924 887
29 95 157 277 285 335 413 616 541 393 669 681 797 736 925 931
30 101 158 297 286 343 414 639 542 408 670 700 798 749 926 939
31 159 159 394 287 432 415 725 543 532 671 774 799 829 927 972
32 6 160 64 288 66 416 294 544 70 672 295 800 360 928 705
33 17 161 106 289 136 417 365 545 168 673 430 801 485 929 771
34 23 162 119 290 149 418 369 546 176 674 442 802 502 930 779
35 40 163 174 291 211 419 482 547 267 675 556 803 601 931 855
36 19 164 124 292 160 420 395 548 190 676 474 804 538 932 805
37 45 165 183 293 226 421 503 549 288 677 573 805 623 933 866
38 49 166 197 294 241 422 518 550 301 678 580 806 637 934 878
39 89 167 276 295 334 423 609 551 383 679 682 807 739 935 926
40 29 168 142 296 173 424 427 552 200 680 488 808 542 936 815
41 55 169 209 297 248 425 522 553 308 681 593 809 643 937 882
42 59 170 217 298 258 426 533 554 318 682 603 810 655 938 892
43 96 171 285 299 344 427 638 555 419 683 696 811 746 939 936
44 72 172 232 300 268 428 565 556 332 684 630 812 663 940 899
45 108 173 306 301 364 429 624 557 426 685 710 813 759 941 941
46 113 174 322 302 379 430 666 558 439 686 718 814 769 942 950
47 172 175 416 303 468 431 751 559 536 687 803 815 850 943 980
48 34 176 156 304 180 432 448 560 206 688 509 816 548 944 839
49 61 177 225 305 266 433 546 561 326 689 613 817 661 945 895
50 74 178 240 306 280 434 572 562 340 690 633 818 679 946 906
51 111 179 311 307 363 435 662 563 437 691 715 819 768 947 945
52 78 180 252 308 292 436 588 564 359 692 650 820 703 948 917
53 120 181 329 309 387 437 676 565 455 693 735 821 781 949 955
54 129 182 342 310 399 438 688 566 476 694 742 822 795 950 959
55 187 183 433 311 494 439 770 567 558 695 820 823 864 951 987
56 84 184 270 312 314 440 605 568 371 696 659 824 716 952 923
57 131 185 348 313 411 441 693 569 469 697 747 825 804 953 965
58 141 186 366 314 418 442 692 570 491 698 764 826 812 954 968
59 208 187 453 315 519 443 790 571 584 699 836 827 873 955 993
60 146 188 386 316 443 444 722 572 493 700 789 828 826 956 975
61 218 189 473 317 528 445 801 573 599 701 854 829 889 957 996
62 236 190 511 318 555 446 814 574 618 702 871 830 900 958 998
63 333 191 585 319 664 447 879 575 745 703 925 831 944 959 1008
64 9 192 71 320 79 448 325 576 107 704 315 832 376 960 733
65 22 193 121 321 165 449 388 577 189 705 463 833 537 961 784
66 26 194 137 322 166 450 423 578 198 706 479 834 540 962 811
67 54 195 201 323 246 451 524 579 303 707 598 835 641 963 883
68 30 196 152 324 181 452 447 580 205 708 495 836 549 964 832
69 58 197 215 325 261 453 534 581 319 709 607 837 652 965 890
70 68 198 231 326 273 454 554 582 331 710 626 838 668 966 896
71 103 199 309 327 358 455 649 583 421 711 713 839 762 967 942
72 36 200 161 328 188 456 465 584 229 712 539 840 563 968 843
73 75 201 234 329 281 457 574 585 339 713 631 841 684 969 908
74 62 202 244 330 286 458 569 586 351 714 644 842 697 970 912
75 114 203 323 331 389 459 673 587 454 715 738 843 785 971 952
76 82 204 255 332 302 460 591 588 377 716 653 844 711 972 920
77 123 205 341 333 400 461 671 589 475 717 744 845 792 973 956
78 135 206 356 334 412 462 691 590 486 718 758 846 808 974 967
79 193 207 449 335 513 463 782 591 575 719 833 847 876 975 990
80 44 208 177 336 235 464 484 592 245 720 547 848 629 976 861
81 73 209 250 337 296 465 589 593 353 721 651 849 702 977 918
82 83 210 264 338 313 466 610 594 372 722 658 850 720 978 927
83 130 211 346 339 402 467 687 595 470 723 755 851 796 979 964
84 91 212 284 340 324 468 620 596 396 724 683 852 732 980 938
85 138 213 368 341 422 469 694 597 492 725 763 853 817 981 970
86 145 214 382 342 444 470 723 598 497 726 783 854 827 982 971
87 214 215 480 343 526 471 806 599 594 727 852 855 886 983 997
88 99 216 293 344 350 472 647 600 420 728 704 856 761 984 948
89 148 217 390 345 445 473 729 601 498 729 788 857 831 985 977
90 163 218 403 346 464 474 740 602 506 730 797 858 840 986 979
91 228 219 496 347 550 475 818 603 617 731 860 859 898 987 999
92 171 220 425 348 481 476 760 604 545 732 813 860 857 988 985
93 242 221 520 349 576 477 834 605 632 733 880 861 910 989 1004
94 254 222 531 350 587 478 844 606 656 734 888 862 915 990 1006
95 357 223 648 351 686 479 905 607 753 735 933 863 960 991 1016
96 51 224 194 352 259 480 512 608 262 736 561 864 654 992 877
97 87 225 279 353 327 481 615 609 384 737 689 865 734 993 934
98 97 226 287 354 345 482 635 610 409 738 698 866 748 994 937
99 144 227 375 355 431 483 724 611 500 739 775 867 821 995 973
100 109 228 312 356 362 484 665 612 415 740 719 868 767 996 951
101 154 229 392 357 452 485 726 613 515 741 791 869 847 997 978
102 167 230 406 358 466 486 756 614 529 742 800 870 853 998 982
103 239 231 505 359 568 487 824 615 625 743 867 871 902 999 1001
104 118 232 336 360 381 488 677 616 440 744 731 872 777 1000 957
105 169 233 410 361 478 489 754 617 544 745 810 873 841 1001 986
106 186 234 434 362 490 490 772 618 559 746 825 874 863 1002 988
107 253 235 523 363 592 491 848 619 645 747 884 875 914 1003 1005
108 195 236 459 364 514 492 786 620 581 748 838 876 874 1004 994
109 269 237 535 365 604 493 837 621 667 749 894 877 922 1005 1007
110 282 238 567 366 619 494 870 622 675 750 907 878 932 1006 1012
111 380 239 670 367 707 495 924 623 773 751 949 879 969 1007 1018
112 133 240 355 368 404 496 680 624 457 752 766 880 799 1008 962
113 191 241 436 369 510 497 780 625 566 753 819 881 869 1009 992
114 213 242 461 370 521 498 798 626 583 754 846 882 881 1010 995
115 275 243 552 371 612 499 856 627 674 755 897 883 928 1011 1009
116 216 244 471 372 527 500 809 628 606 756 858 884 891 1012 1000
117 283 245 571 373 628 501 875 629 685 757 911 885 935 1013 1010
118 299 246 590 374 608 502 865 630 709 758 916 886 943 1014 1013
119 401 247 695 375 721 503 930 631 787 759 961 887 976 1015 1019
120 233 248 508 376 557 504 828 632 634 760 868 888 904 1016 1002
121 307 249 595 377 660 505 885 633 712 761 921 889 947 1017 1014
122 317 250 611 378 672 506 893 634 730 762 929 890 953 1018 1015
123 417 251 690 379 750 507 946 635 807 763 966 891 981 1019 1020
124 337 252 627 380 678 508 909 636 741 764 940 892 958 1020 1017
125 435 253 714 381 778 509 954 637 822 765 974 893 989 1021 1021
126 460 254 743 382 794 510 963 638 842 766 983 894 991 1022 1022
127 577 255 816 383 845 511 984 639 903 767 1003 895 1011 1023 1023
Sequence Z7, having a sequence length of 512:
[0, 1, 2, 7, 3, 8, 11, 24, 4, 10, 13, 27, 16, 30, 34, 70, 5, 12, 14, 31, 21, 37, 45, 73, 20, 44, 41, 81, 54, 88, 93, 141, 6, 17, 23, 39, 19, 43, 47, 82, 28, 52, 56, 89, 65, 99, 103, 152, 33, 57, 67, 101, 71, 109, 116, 165, 77, 118, 126, 177, 131, 187, 199, 269, 9, 22, 26, 51, 29, 55, 62, 95, 35, 68, 58, 104, 75, 112, 121, 169, 42, 66, 76, 117, 84, 124, 130, 183, 91, 133, 145, 193, 151, 205, 215, 286, 49, 80, 90, 129, 100, 137, 149, 202, 107, 150, 164, 214, 171, 225, 234, 299, 119, 167, 182, 228, 185, 235, 247, 313, 196, 252, 259, 323, 273, 334, 347, 406, 15, 25, 32, 63, 38, 69, 74, 120, 46, 79, 85, 128, 92, 136, 140, 201, 53, 86, 94, 138, 102, 146, 155, 210, 111, 161, 168, 220, 179, 230, 245, 309, 60, 98, 108, 154, 113, 162, 173, 229, 127, 178, 186, 237, 195, 251, 262, 322, 139, 190, 203, 254, 213, 268, 275, 332, 226, 281, 293, 345, 302, 356, 372, 407, 64, 110, 123, 174, 135, 184, 194, 253, 143, 197, 206, 263, 216, 274, 285, 342, 156, 211, 221, 279, 236, 295, 301, 358, 242, 306, 315, 366, 327, 378, 387, 435, 170, 231, 239, 297, 255, 308, 317, 369, 272, 319, 333, 381, 346, 390, 398, 442, 284, 335, 348, 393, 355, 402, 412, 458, 370, 415, 422, 453, 429, 460, 469, 488, 18, 36, 40, 83, 48, 87, 96, 144, 50, 97, 105, 158, 114, 172, 175, 246, 59, 106, 115, 176, 125, 181, 189, 248, 132, 188, 200, 261, 212, 271, 276, 331, 61, 122, 134, 180, 142, 191, 204, 270, 153, 209, 217, 277, 224, 291, 298, 354, 159, 223, 232, 290, 241, 303, 311, 365, 257, 320, 324, 377, 336, 386, 395, 439, 72, 147, 148, 207, 160, 219, 227, 287, 166, 233, 238, 305, 249, 312, 321, 374, 198, 244, 256, 314, 264, 325, 337, 384, 283, 338, 350, 392, 359, 405, 409, 450, 218, 266, 278, 330, 289, 344, 352, 399, 300, 357, 364, 414, 375, 417, 426, 459, 316, 371, 379, 423, 385, 430, 419, 461, 396, 437, 444, 470, 448, 477, 482, 495, 78, 157, 163, 240, 192, 250, 258, 318, 208, 260, 267, 329, 282, 339, 349, 401, 222, 280, 288, 343, 294, 353, 361, 408, 307, 363, 367, 416, 383, 425, 433, 465, 243, 292, 296, 360, 310, 368, 376, 420, 328, 380, 388, 432, 397, 428, 441, 471, 341, 391, 403, 438, 410, 446, 452, 475, 418, 456, 455, 481, 462, 484, 487, 501, 265, 304, 326, 382, 340, 389, 394, 436, 351, 404, 400, 445, 413, 443, 454, 479, 362, 411, 421, 451, 427, 457, 463, 485, 434, 467, 468, 489, 474, 492, 494, 504, 373, 424, 431, 464, 440, 466, 473, 490, 447, 472, 476, 496, 480, 493, 499, 506, 449, 478, 483, 497, 486, 500, 498, 507, 491, 502, 503, 508, 505, 509, 510, 511]
TABLE Z7
having a sequence length of 512:
Relia- Relia- Relia- Relia- Relia- Relia- Relia- Relia-
Polar- bility Polar- bility Polar- bility Polar- bility Polar- bility Polar- bility Polar- bility Polar- bility
ized or ized or ized or ized or ized or ized or ized or ized or
chan- se- chan- se- chan- se- chan- se- chan- se- chan- se- chan- se- chan- se-
nel quence nel quence nel quence nel quence nel quence nel quence nel quence nel quence
se- num- se- num- se- num- se- num- se- num- se- num- se- num- se- num-
quen- ber quen- ber quen- ber quen- ber quen- ber quen- ber quen- ber quen- ber
ce of ce of ce of ce of ce of ce of ce of ce of
num- relia- num- relia- num- relia- num- relia- num- relia- num- relia- num- relia- num- relia-
ber bility ber bility ber bility ber bility ber bility ber bility ber bility ber bility
0 0 64 9 128 15 192 64 256 18 320 72 384 78 448 265
1 1 65 22 129 25 193 110 257 36 321 147 385 157 449 304
2 2 66 26 130 32 194 123 258 40 322 148 386 163 450 326
3 7 67 51 131 63 195 174 259 83 323 207 387 240 451 382
4 3 68 29 132 38 196 135 260 48 324 160 388 192 452 340
5 8 69 55 133 69 197 184 261 87 325 219 389 250 453 389
6 11 70 62 134 74 198 194 262 96 326 227 390 258 454 394
7 24 71 95 135 120 199 253 263 144 327 287 391 318 455 436
8 4 72 35 136 46 200 143 264 50 328 166 392 208 456 351
9 10 73 68 137 79 201 197 265 97 329 233 393 260 457 404
10 13 74 58 138 85 202 206 266 105 330 238 394 267 458 400
11 27 75 104 139 128 203 263 267 158 331 305 395 329 459 445
12 16 76 75 140 92 204 216 268 114 332 249 396 282 460 413
13 30 77 112 141 136 205 274 269 172 333 312 397 339 461 443
14 34 78 121 142 140 206 285 270 175 334 321 398 349 462 454
15 70 79 169 143 201 207 342 271 246 335 374 399 401 463 479
16 5 80 42 144 53 208 156 272 59 336 198 400 222 464 362
17 12 81 66 145 86 209 211 273 106 337 244 401 280 465 411
18 14 82 76 146 94 210 221 274 115 338 256 402 288 466 421
19 31 83 117 147 138 211 279 275 176 339 314 403 343 467 451
20 21 84 84 148 102 212 236 276 125 340 264 404 294 468 427
21 37 85 124 149 146 213 295 277 181 341 325 405 353 469 457
22 45 86 130 150 155 214 301 278 189 342 337 406 361 470 463
23 73 87 183 151 210 215 358 279 248 343 384 407 408 471 485
24 20 88 91 152 111 216 242 280 132 344 283 408 307 472 434
25 44 89 133 153 161 217 306 281 188 345 338 409 363 473 467
26 41 90 145 154 168 218 315 282 200 346 350 410 367 474 468
27 81 91 193 155 220 219 366 283 261 347 392 411 416 475 489
28 54 92 151 156 179 220 327 284 212 348 359 412 383 476 474
29 88 93 205 157 230 221 378 285 271 349 405 413 425 477 492
30 93 94 215 158 245 222 387 286 276 350 409 414 433 478 494
31 141 95 286 159 309 223 435 287 331 351 450 415 465 479 504
32 6 96 49 160 60 224 170 288 61 352 218 416 243 480 373
33 17 97 80 161 98 225 231 289 122 353 266 417 292 481 424
34 23 98 90 162 108 226 239 290 134 354 278 418 296 482 431
35 39 99 129 163 154 227 297 291 180 355 330 419 360 483 464
36 19 100 100 164 113 228 255 292 142 356 289 420 310 484 440
37 43 101 137 165 162 229 308 293 191 357 344 421 368 485 466
38 47 102 149 166 173 230 317 294 204 358 352 422 376 486 473
39 82 103 202 167 229 231 369 295 270 359 399 423 420 487 490
40 28 104 107 168 127 232 272 296 153 360 300 424 328 488 447
41 52 105 150 169 178 233 319 297 209 361 357 425 380 489 472
42 56 106 164 170 186 234 333 298 217 362 364 426 388 490 476
43 89 107 214 171 237 235 381 299 277 363 414 427 432 491 496
44 65 108 171 172 195 236 346 300 224 364 375 428 397 492 480
45 99 109 225 173 251 237 390 301 291 365 417 429 428 493 493
46 103 110 234 174 262 238 398 302 298 366 426 430 441 494 499
47 152 111 299 175 322 239 442 303 354 367 459 431 471 495 506
48 33 112 119 176 139 240 284 304 159 368 316 432 341 496 449
49 57 113 167 177 190 241 335 305 223 369 371 433 391 497 478
50 67 114 182 178 203 242 348 306 232 370 379 434 403 498 483
51 101 115 228 179 254 243 393 307 290 371 423 435 438 499 497
52 71 116 185 180 213 244 355 308 241 372 385 436 410 500 486
53 109 117 235 181 268 245 402 309 303 373 430 437 446 501 500
54 116 118 247 182 275 246 412 310 311 374 419 438 452 502 498
55 165 119 313 183 332 247 458 311 365 375 461 439 475 503 507
56 77 120 196 184 226 248 370 312 257 376 396 440 418 504 491
57 118 121 252 185 281 249 415 313 320 377 437 441 456 505 502
58 126 122 259 186 293 250 422 314 324 378 444 442 455 506 503
59 177 123 323 187 345 251 453 315 377 379 470 443 481 507 508
60 131 124 273 188 302 252 429 316 336 380 448 444 462 508 505
61 187 125 334 189 356 253 460 317 386 381 477 445 484 509 509
62 199 126 347 190 372 254 469 318 395 382 482 446 487 510 510
63 269 127 406 191 407 255 488 319 439 383 495 447 501 511 511
Sequence Z8, having a sequence length of 256:
[0, 1, 2, 7, 3, 8, 11, 23, 4, 10, 13, 26, 16, 29, 33, 63, 5, 12, 14, 30, 20, 35, 42, 65, 19, 41, 38, 72, 49, 77, 82, 120, 6, 17, 22, 37, 18, 40, 44, 73, 27, 47, 51, 78, 58, 86, 90, 127, 32, 52, 60, 88, 64, 94, 99, 134, 69, 101, 107, 142, 112, 150, 157, 194, 9, 21, 25, 46, 28, 50, 55, 84, 34, 61, 53, 91, 67, 97, 104, 137, 39, 59, 68, 100, 74, 106, 111, 146, 80, 113, 122, 152, 126, 161, 167, 203, 45, 71, 79, 110, 87, 116, 124, 159, 92, 125, 133, 166, 139, 171, 177, 207, 102, 135, 145, 173, 148, 178, 184, 213, 155, 186, 190, 218, 196, 222, 227, 243, 15, 24, 31, 56, 36, 62, 66, 103, 43, 70, 75, 109, 81, 115, 119, 158, 48, 76, 83, 117, 89, 123, 129, 163, 96, 131, 136, 169, 144, 175, 183, 212, 54, 85, 93, 128, 98, 132, 140, 174, 108, 143, 149, 180, 154, 185, 191, 217, 118, 151, 160, 188, 165, 193, 198, 220, 172, 200, 204, 225, 209, 230, 235, 244, 57, 95, 105, 141, 114, 147, 153, 187, 121, 156, 162, 192, 168, 197, 202, 224, 130, 164, 170, 199, 179, 205, 208, 231, 182, 210, 214, 232, 219, 236, 238, 249, 138, 176, 181, 206, 189, 211, 215, 233, 195, 216, 221, 237, 226, 239, 241, 250, 201, 223, 228, 240, 229, 242, 245, 252, 234, 246, 247, 251, 248, 253, 254, 255]
TABLE Z8
having a sequence length of 256:
Relia- Relia- Relia- Relia- Relia- Relia- Relia- Relia-
Polar- bility Polar- bility Polar- bility Polar- bility Polar- bility Polar- bility Polar- bility Polar- bility
ized or ized or ized or ized or ized or ized or ized or ized or
chan- se- chan- se- chan- se- chan- se- chan- se- chan- se- chan- se- chan- se-
nel quence nel quence nel quence nel quence nel quence nel quence nel quence nel quence
se- num- se- num- se- num- se- num- se- num- se- num- se- num- se- num-
quen- ber quen- ber quen- ber quen- ber quen- ber quen- ber quen- ber quen- ber
ce of ce of ce of ce of ce of ce of ce of ce of
num- relia- num- relia- num- relia- num- relia- num- relia- num- relia- num- relia- num- relia-
ber bility ber bility ber bility ber bility ber bility ber bility ber bility ber bility
0 0 32 6 64 9 96 45 128 15 160 54 192 57 224 138
1 1 33 17 65 21 97 71 129 24 161 85 193 95 225 176
2 2 34 22 66 25 98 79 130 31 162 93 194 105 226 181
3 7 35 37 67 46 99 110 131 56 163 128 195 141 227 206
4 3 36 18 68 28 100 87 132 36 164 98 196 114 228 189
5 8 37 40 69 50 101 116 133 62 165 132 197 147 229 211
6 11 38 44 70 55 102 124 134 66 166 140 198 153 230 215
7 23 39 73 71 84 103 159 135 103 167 174 199 187 231 233
8 4 40 27 72 34 104 92 136 43 168 108 200 121 232 195
9 10 41 47 73 61 105 125 137 70 169 143 201 156 233 216
10 13 42 51 74 53 106 133 138 75 170 149 202 162 234 221
11 26 43 78 75 91 107 166 139 109 171 180 203 192 235 237
12 16 44 58 76 67 108 139 140 81 172 154 204 168 236 226
13 29 45 86 77 97 109 171 141 115 173 185 205 197 237 239
14 33 46 90 78 104 110 177 142 119 174 191 206 202 238 241
15 63 47 127 79 137 111 207 143 158 175 217 207 224 239 250
16 5 48 32 80 39 112 102 144 48 176 118 208 130 240 201
17 12 49 52 81 59 113 135 145 76 177 151 209 164 241 223
18 14 50 60 82 68 114 145 146 83 178 160 210 170 242 228
19 30 51 88 83 100 115 173 147 117 179 188 211 199 243 240
20 20 52 64 84 74 116 148 148 89 180 165 212 179 244 229
21 35 53 94 85 106 117 178 149 123 181 193 213 205 245 242
22 42 54 99 86 111 118 184 150 129 182 198 214 208 246 245
23 65 55 134 87 146 119 213 151 163 183 220 215 231 247 252
24 19 56 69 88 80 120 155 152 96 184 172 216 182 248 234
25 41 57 101 89 113 121 186 153 131 185 200 217 210 249 246
26 38 58 107 90 122 122 190 154 136 186 204 218 214 250 247
27 72 59 142 91 152 123 218 155 169 187 225 219 232 251 251
28 49 60 112 92 126 124 196 156 144 188 209 220 219 252 248
29 77 61 150 93 161 125 222 157 175 189 230 221 236 253 253
30 82 62 157 94 167 126 227 158 183 190 235 222 238 254 254
31 120 63 194 95 203 127 243 159 212 191 244 223 249 255 255
Sequence Z9, having a sequence length of 128:
[0, 1, 2, 7, 3, 8, 11, 22, 4, 10, 13, 24, 15, 27, 30, 53, 5, 12, 14, 28, 19, 32, 38, 55, 18, 37, 34, 60, 43, 63, 67, 89, 6, 16, 21, 33, 17, 36, 39, 61, 25, 42, 45, 64, 49, 69, 72, 94, 29, 46, 51, 71, 54, 75, 77, 96, 58, 79, 83, 100, 86, 104, 107, 119, 9, 20, 23, 41, 26, 44, 48, 68, 31, 52, 47, 73, 56, 76, 81, 98, 35, 50, 57, 78, 62, 82, 85, 102, 66, 87, 90, 105, 93, 109, 111, 121, 40, 59, 65, 84, 70, 88, 91, 108, 74, 92, 95, 110, 99, 112, 114, 122, 80, 97, 101, 113, 103, 115, 116, 123, 106, 117, 118, 124, 120, 125, 126, 127]
TABLE Z9
having a sequence length of 128:
Relia- Relia- Relia- Relia- Relia- Relia- Relia- Relia-
Polar- bility Polar- bility Polar- bility Polar- bility Polar- bility Polar- bility Polar- bility Polar- bility
ized or ized or ized or ized or ized or ized or ized or ized or
chan- se- chan- se- chan- se- chan- se- chan- se- chan- se- chan- se- chan- se-
nel quence nel quence nel quence nel quence nel quence nel quence nel quence nel quence
se- num- se- num- se- num- se- num- se- num- se- num- se- num- se- num-
quen- ber quen- ber quen- ber quen- ber quen- ber quen- ber quen- ber quen- ber
ce of ce of ce of ce of ce of ce of ce of ce of
num- relia- num- relia- num- relia- num- relia- num- relia- num- relia- num- relia- num- relia-
ber bility ber bility ber bility ber bility ber bility ber bility ber bility ber bility
0 0 16 5 32 6 48 29 64 9 80 35 96 40 112 80
1 1 17 12 33 16 49 46 65 20 81 50 97 59 113 97
2 2 18 14 34 21 50 51 66 23 82 57 98 65 114 101
3 7 19 28 35 33 51 71 67 41 83 78 99 84 115 113
4 3 20 19 36 17 52 54 68 26 84 62 100 70 116 103
5 8 21 32 37 36 53 75 69 44 85 82 101 88 117 115
6 11 22 38 38 39 54 77 70 48 86 85 102 91 118 116
7 22 23 55 39 61 55 96 71 68 87 102 103 108 119 123
8 4 24 18 40 25 56 58 72 31 88 66 104 74 120 106
9 10 25 37 41 42 57 79 73 52 89 87 105 92 121 117
10 13 26 34 42 45 58 83 74 47 90 90 106 95 122 118
11 24 27 60 43 64 59 100 75 73 91 105 107 110 123 124
12 15 28 43 44 49 60 86 76 56 92 93 108 99 124 120
13 27 29 63 45 69 61 104 77 76 93 109 109 112 125 125
14 30 30 67 46 72 62 107 78 81 94 111 110 114 126 126
15 53 31 89 47 94 63 119 79 98 95 121 111 122 127 127
Sequence Z10, having a sequence length of 64:
[0, 1, 2, 7, 3, 8, 10, 20, 4, 9, 12, 21, 14, 23, 26, 40, 5, 11, 13, 24, 18, 27, 32, 42, 17, 31, 29, 44, 35, 46, 48, 57, 6, 15, 19, 28, 16, 30, 33, 45, 22, 34, 36, 47, 38, 49, 51, 58, 25, 37, 39, 50, 41, 52, 53, 59, 43, 54, 55, 60, 56, 61, 62, 63]
TABLE Z10
having a sequence length of 64:
Relia- Relia- Relia- Relia- Relia- Relia- Relia- Relia-
Polar- bility Polar- bility Polar- bility Polar- bility Polar- bility Polar- bility Polar- bility Polar- bility
ized or ized or ized or ized or ized or ized or ized or ized or
chan- se- chan- se- chan- se- chan- se- chan- se- chan- se- chan- se- chan- se-
nel quence nel quence nel quence nel quence nel quence nel quence nel quence nel quence
se- num- se- num- se- num- se- num- se- num- se- num- se- num- se- num-
quen- ber quen- ber quen- ber quen- ber quen- ber quen- ber quen- ber quen- ber
ce of ce of ce of ce of ce of ce of ce of ce of
num- relia- num- relia- num- relia- num- relia- num- relia- num- relia- num- relia- num- relia-
ber bility ber bility ber bility ber bility ber bility ber bility ber bility ber bility
0 0 8 4 16 5 24 17 32 6 40 22 48 25 56 43
1 1 9 9 17 11 25 31 33 15 41 34 49 37 57 54
2 2 10 12 18 13 26 29 34 19 42 36 50 39 58 55
3 7 11 21 19 24 27 44 35 28 43 47 51 50 59 60
4 3 12 14 20 18 28 35 36 16 44 38 52 41 60 56
5 8 13 23 21 27 29 46 37 30 45 49 53 52 61 61
6 10 14 26 22 32 30 48 38 33 46 51 54 53 62 62
7 20 15 40 23 42 31 57 39 45 47 58 55 59 63 63
Third group of sequences (a criterion that comprehensively considers performance obtained by List (list) whose sizes are respectively 1, 2, 4, 8, and 16, and preferentially considers performance of Lists 2, 4, and 8).
Sequence Q11, having a sequence length of 1024:
[0, 1, 2, 4, 8, 16, 32, 3, 5, 64, 9, 6, 17, 10, 18, 128, 12, 33, 65, 20, 256, 34, 24, 36, 7, 129, 66, 512, 11, 40, 68, 130, 19, 13, 48, 14, 72, 257, 21, 132, 35, 258, 26, 513, 80, 37, 25, 22, 136, 260, 264, 38, 514, 96, 67, 41, 144, 28, 69, 42, 516, 49, 74, 272, 160, 520, 288, 528, 192, 544, 70, 44, 131, 81, 50, 73, 15, 320, 133, 52, 23, 134, 384, 76, 137, 82, 56, 27, 97, 39, 259, 84, 138, 145, 261, 29, 43, 98, 515, 88, 140, 30, 146, 71, 262, 265, 161, 576, 45, 100, 640, 51, 148, 46, 75, 266, 273, 517, 104, 162, 53, 193, 152, 77, 164, 768, 268, 274, 518, 54, 83, 57, 521, 112, 135, 78, 289, 194, 85, 276, 522, 58, 168, 139, 99, 86, 60, 280, 89, 290, 529, 524, 196, 141, 101, 147, 176, 142, 530, 321, 31, 200, 90, 545, 292, 322, 532, 263, 149, 102, 105, 304, 296, 163, 92, 47, 267, 385, 546, 324, 208, 386, 150, 153, 165, 106, 55, 328, 536, 577, 548, 113, 154, 79, 269, 108, 578, 224, 166, 519, 552, 195, 270, 641, 523, 275, 580, 291, 59, 169, 560, 114, 277, 156, 87, 197, 116, 170, 61, 531, 525, 642, 281, 278, 526, 177, 293, 388, 91, 584, 769, 198, 172, 120, 201, 336, 62, 282, 143, 103, 178, 294, 93, 644, 202, 592, 323, 392, 297, 770, 107, 180, 151, 209, 284, 648, 94, 204, 298, 400, 608, 352, 325, 533, 155, 210, 305, 547, 300, 109, 184, 534, 537, 115, 167, 225, 326, 306, 772, 157, 656, 329, 110, 117, 212, 171, 776, 330, 226, 549, 538, 387, 308, 216, 416, 271, 279, 158, 337, 550, 672, 118, 332, 579, 540, 389, 173, 121, 553, 199, 784, 179, 228, 338, 312, 704, 390, 174, 554, 581, 393, 283, 122, 448, 353, 561, 203, 63, 340, 394, 527, 582, 556, 181, 295, 285, 232, 124, 205, 182, 643, 562, 286, 585, 299, 354, 211, 401, 185, 396, 344, 586, 645, 593, 535, 240, 206, 95, 327, 564, 800, 402, 356, 307, 301, 417, 213, 568, 832, 588, 186, 646, 404, 227, 896, 594, 418, 302, 649, 771, 360, 539, 111, 331, 214, 309, 188, 449, 217, 408, 609, 596, 551, 650, 229, 159, 420, 310, 541, 773, 610, 657, 333, 119, 600, 339, 218, 368, 652, 230, 391, 313, 450, 542, 334, 233, 555, 774, 175, 123, 658, 612, 341, 777, 220, 314, 424, 395, 673, 583, 355, 287, 183, 234, 125, 557, 660, 616, 342, 316, 241, 778, 563, 345, 452, 397, 403, 207, 674, 558, 785, 432, 357, 187, 236, 664, 624, 587, 780, 705, 126, 242, 565, 398, 346, 456, 358, 405, 303, 569, 244, 595, 189, 566, 676, 361, 706, 589, 215, 786, 647, 348, 419, 406, 464, 680, 801, 362, 590, 409, 570, 788, 597, 572, 219, 311, 708, 598, 601, 651, 421, 792, 802, 611, 602, 410, 231, 688, 653, 248, 369, 190, 364, 654, 659, 335, 480, 315, 221, 370, 613, 422, 425, 451, 614, 543, 235, 412, 343, 372, 775, 317, 222, 426, 453, 237, 559, 833, 804, 712, 834, 661, 808, 779, 617, 604, 433, 720, 816, 836, 347, 897, 243, 662, 454, 318, 675, 618, 898, 781, 376, 428, 665, 736, 567, 840, 625, 238, 359, 457, 399, 787, 591, 678, 434, 677, 349, 245, 458, 666, 620, 363, 127, 191, 782, 407, 436, 626, 571, 465, 681, 246, 707, 350, 599, 668, 790, 460, 249, 682, 573, 411, 803, 789, 709, 365, 440, 628, 689, 374, 423, 466, 793, 250, 371, 481, 574, 413, 603, 366, 468, 655, 900, 805, 615, 684, 710, 429, 794, 252, 373, 605, 848, 690, 713, 632, 482, 806, 427, 904, 414, 223, 663, 692, 835, 619, 472, 455, 796, 809, 714, 721, 837, 716, 864, 810, 606, 912, 722, 696, 377, 435, 817, 319, 621, 812, 484, 430, 838, 667, 488, 239, 378, 459, 622, 627, 437, 380, 818, 461, 496, 669, 679, 724, 841, 629, 351, 467, 438, 737, 251, 462, 442, 441, 469, 247, 683, 842, 738, 899, 670, 783, 849, 820, 728, 928, 791, 367, 901, 630, 685, 844, 633, 711, 253, 691, 824, 902, 686, 740, 850, 375, 444, 470, 483, 415, 485, 905, 795, 473, 634, 744, 852, 960, 865, 693, 797, 906, 715, 807, 474, 636, 694, 254, 717, 575, 913, 798, 811, 379, 697, 431, 607, 489, 866, 723, 486, 908, 718, 813, 476, 856, 839, 725, 698, 914, 752, 868, 819, 814, 439, 929, 490, 623, 671, 739, 916, 463, 843, 381, 497, 930, 821, 726, 961, 872, 492, 631, 729, 700, 443, 741, 845, 920, 382, 822, 851, 730, 498, 880, 742, 445, 471, 635, 932, 687, 903, 825, 500, 846, 745, 826, 732, 446, 962, 936, 475, 853, 867, 637, 907, 487, 695, 746, 828, 753, 854, 857, 504, 799, 255, 964, 909, 719, 477, 915, 638, 748, 944, 869, 491, 699, 754, 858, 478, 968, 383, 910, 815, 976, 870, 917, 727, 493, 873, 701, 931, 756, 860, 499, 731, 823, 922, 874, 918, 502, 933, 743, 760, 881, 494, 702, 921, 501, 876, 847, 992, 447, 733, 827, 934, 882, 937, 963, 747, 505, 855, 924, 734, 829, 965, 938, 884, 506, 749, 945, 966, 755, 859, 940, 830, 911, 871, 639, 888, 479, 946, 750, 969, 508, 861, 757, 970, 919, 875, 862, 758, 948, 977, 923, 972, 761, 877, 952, 495, 703, 935, 978, 883, 762, 503, 925, 878, 735, 993, 885, 939, 994, 980, 926, 764, 941, 967, 886, 831, 947, 507, 889, 984, 751, 942, 996, 971, 890, 509, 949, 973, 1000, 892, 950, 863, 759, 1008, 510, 979, 953, 763, 974, 954, 879, 981, 982, 927, 995, 765, 956, 887, 985, 997, 986, 943, 891, 998, 766, 511, 988, 1001, 951, 1002, 893, 975, 894, 1009, 955, 1004, 1010, 957, 983, 958, 987, 1012, 999, 1016, 767, 989, 1003, 990, 1005, 959, 1011, 1013, 895, 1006, 1014, 1017, 1018, 991, 1020, 1007, 1015, 1019, 1021, 1022, 1023]
TABLE Q11
having a sequence length of 1024:
Relia- Relia- Relia- Relia- Relia- Relia- Relia- Relia-
bility Polar- bility Polar- bility Polar- bility Polar- bility Polar- bility Polar- bility Polar- bility Polar-
or ized or ized or ized or ized or ized or ized or ized or ized
se- chan- se- chan- se- chan- se- chan- se- chan- se- chan- se- chan- se- chan-
quence nel quence nel quence nel quence nel quence nel quence nel quence nel quence nel
num- se- num- se- num- se- num- se- num- se- num- se- num- se- num- se-
ber quen- ber quen- ber quen- ber quen- ber quen- ber quen- ber quen- ber quen-
of ce of ce of ce of ce of ce of ce of ce of ce
relia- num- relia- num- relia- num- relia- num- relia- num- relia- num- relia- num- relia- num-
bility ber bility ber bility ber bility ber bility ber bility ber bility ber bility ber
0 0 128 518 256 94 384 214 512 364 640 414 768 819 896 966
1 1 129 54 257 204 385 309 513 654 641 223 769 814 897 755
2 2 130 83 258 298 386 188 514 659 642 663 770 439 898 859
3 4 131 57 259 400 387 449 515 335 643 692 771 929 899 940
4 8 132 521 260 608 388 217 516 480 644 835 772 490 900 830
5 16 133 112 261 352 389 408 517 315 645 619 773 623 901 911
6 32 134 135 262 325 390 609 518 221 646 472 774 671 902 871
7 3 135 78 263 533 391 596 519 370 647 455 775 739 903 639
8 5 136 289 264 155 392 551 520 613 648 796 776 916 904 888
9 64 137 194 265 210 393 650 521 422 649 809 777 463 905 479
10 9 138 85 266 305 394 229 522 425 650 714 778 843 906 946
11 6 139 276 267 547 395 159 523 451 651 721 779 381 907 750
12 17 140 522 268 300 396 420 524 614 652 837 780 497 908 969
13 10 141 58 269 109 397 310 525 543 653 716 781 930 909 508
14 18 142 168 270 184 398 541 526 235 654 864 782 821 910 861
15 128 143 139 271 534 399 773 527 412 655 810 783 726 911 757
16 12 144 99 272 537 400 610 528 343 656 606 784 961 912 970
17 33 145 86 273 115 401 657 529 372 657 912 785 872 913 919
18 65 146 60 274 167 402 333 530 775 658 722 786 492 914 875
19 20 147 280 275 225 403 119 531 317 659 696 787 631 915 862
20 256 148 89 276 326 404 600 532 222 660 377 788 729 916 758
21 34 149 290 277 306 405 339 533 426 661 435 789 700 917 948
22 24 150 529 278 772 406 218 534 453 662 817 790 443 918 977
23 36 151 524 279 157 407 368 535 237 663 319 791 741 919 923
24 7 152 196 280 656 408 652 536 559 664 621 792 845 920 972
25 129 153 141 281 329 409 230 537 833 665 812 793 920 921 761
26 66 154 101 282 110 410 391 538 804 666 484 794 382 922 877
27 512 155 147 283 117 411 313 539 712 667 430 795 822 923 952
28 11 156 176 284 212 412 450 540 834 668 838 796 851 924 495
29 40 157 142 285 171 413 542 541 661 669 667 797 730 925 703
30 68 158 530 286 776 414 334 542 808 670 488 798 498 926 935
31 130 159 321 287 330 415 233 543 779 671 239 799 880 927 978
32 19 160 31 288 226 416 555 544 617 672 378 800 742 928 883
33 13 161 200 289 549 417 774 545 604 673 459 801 445 929 762
34 48 162 90 290 538 418 175 546 433 674 622 802 471 930 503
35 14 163 545 291 387 419 123 547 720 675 627 803 635 931 925
36 72 164 292 292 308 420 658 548 816 676 437 804 932 932 878
37 257 165 322 293 216 421 612 549 836 677 380 805 687 933 735
38 21 166 532 294 416 422 341 550 347 678 818 806 903 934 993
39 132 167 263 295 271 423 777 551 897 679 461 807 825 935 885
40 35 168 149 296 279 424 220 552 243 680 496 808 500 936 939
41 258 169 102 297 158 425 314 553 662 681 669 809 846 937 994
42 26 170 105 298 337 426 424 554 454 682 679 810 745 938 980
43 513 171 304 299 550 427 395 555 318 683 724 811 826 939 926
44 80 172 296 300 672 428 673 556 675 684 841 812 732 940 764
45 37 173 163 301 118 429 583 557 618 685 629 813 446 941 941
46 25 174 92 302 332 430 355 558 898 686 351 814 962 942 967
47 22 175 47 303 579 431 287 559 781 687 467 815 936 943 886
48 136 176 267 304 540 432 183 560 376 688 438 816 475 944 831
49 260 177 385 305 389 433 234 561 428 689 737 817 853 945 947
50 264 178 546 306 173 434 125 562 665 690 251 818 867 946 507
51 38 179 324 307 121 435 557 563 736 691 462 819 637 947 889
52 514 180 208 308 553 436 660 564 567 692 442 820 907 948 984
53 96 181 386 309 199 437 616 565 840 693 441 821 487 949 751
54 67 182 150 310 784 438 342 566 625 694 469 822 695 950 942
55 41 183 153 311 179 439 316 567 238 695 247 823 746 951 996
56 144 184 165 312 228 440 241 568 359 696 683 824 828 952 971
57 28 185 106 313 338 441 778 569 457 697 842 825 753 953 890
58 69 186 55 314 312 442 563 570 399 698 738 826 854 954 509
59 42 187 328 315 704 443 345 571 787 699 899 827 857 955 949
60 516 188 536 316 390 444 452 572 591 700 670 828 504 956 973
61 49 189 577 317 174 445 397 573 678 701 783 829 799 957 1000
62 74 190 548 318 554 446 403 574 434 702 849 830 255 958 892
63 272 191 113 319 581 447 207 575 677 703 820 831 964 959 950
64 160 192 154 320 393 448 674 576 349 704 728 832 909 960 863
65 520 193 79 321 283 449 558 577 245 705 928 833 719 961 759
66 288 194 269 322 122 450 785 578 458 706 791 834 477 962 1008
67 528 195 108 323 448 451 432 579 666 707 367 835 915 963 510
68 192 196 578 324 353 452 357 580 620 708 901 836 638 964 979
69 544 197 224 325 561 453 187 581 363 709 630 837 748 965 953
70 70 198 166 326 203 454 236 582 127 710 685 838 944 966 763
71 44 199 519 327 63 455 664 583 191 711 844 839 869 967 974
72 131 200 552 328 340 456 624 584 782 712 633 840 491 968 954
73 81 201 195 329 394 457 587 585 407 713 711 841 699 969 879
74 50 202 270 330 527 458 780 586 436 714 253 842 754 970 981
75 73 203 641 331 582 459 705 587 626 715 691 843 858 971 982
76 15 204 523 332 556 460 126 588 571 716 824 844 478 972 927
77 320 205 275 333 181 461 242 589 465 717 902 845 968 973 995
78 133 206 580 334 295 462 565 590 681 718 686 846 383 974 765
79 52 207 291 335 285 463 398 591 246 719 740 847 910 975 956
80 23 208 59 336 232 464 346 592 707 720 850 848 815 976 887
81 134 209 169 337 124 465 456 593 350 721 375 849 976 977 985
82 384 210 560 338 205 466 358 594 599 722 444 850 870 978 997
83 76 211 114 339 182 467 405 595 668 723 470 851 917 979 986
84 137 212 277 340 643 468 303 596 790 724 483 852 727 980 943
85 82 213 156 341 562 469 569 597 460 725 415 853 493 981 891
86 56 214 87 342 286 470 244 598 249 726 485 854 873 982 998
87 27 215 197 343 585 471 595 599 682 727 905 855 701 983 766
88 97 216 116 344 299 472 189 600 573 728 795 856 931 984 511
89 39 217 170 345 354 473 566 601 411 729 473 857 756 985 988
90 259 218 61 346 211 474 676 602 803 730 634 858 860 986 1001
91 84 219 531 347 401 475 361 603 789 731 744 859 499 987 951
92 138 220 525 348 185 476 706 604 709 732 852 860 731 988 1002
93 145 221 642 349 396 477 589 605 365 733 960 861 823 989 893
94 261 222 281 350 344 478 215 606 440 734 865 862 922 990 975
95 29 223 278 351 586 479 786 607 628 735 693 863 874 991 894
96 43 224 526 352 645 480 647 608 689 736 797 864 918 992 1009
97 98 225 177 353 593 481 348 609 374 737 906 865 502 993 955
98 515 226 293 354 535 482 419 610 423 738 715 866 933 994 1004
99 88 227 388 355 240 483 406 611 466 739 807 867 743 995 1010
100 140 228 91 356 206 484 464 612 793 740 474 868 760 996 957
101 30 229 584 357 95 485 680 613 250 741 636 869 881 997 983
102 146 230 769 358 327 486 801 614 371 742 694 870 494 998 958
103 71 231 198 359 564 487 362 615 481 743 254 871 702 999 987
104 262 232 172 360 800 488 590 616 574 744 717 872 921 1000 1012
105 265 233 120 361 402 489 409 617 413 745 575 873 501 1001 999
106 161 234 201 362 356 490 570 618 603 746 913 874 876 1002 1016
107 576 235 336 363 307 491 788 619 366 747 798 875 847 1003 767
108 45 236 62 364 301 492 597 620 468 748 811 876 992 1004 989
109 100 237 282 365 417 493 572 621 655 749 379 877 447 1005 1003
110 640 238 143 366 213 494 219 622 900 750 697 878 733 1006 990
111 51 239 103 367 568 495 311 623 805 751 431 879 827 1007 1005
112 148 240 178 368 832 496 708 624 615 752 607 880 934 1008 959
113 46 241 294 369 588 497 598 625 684 753 489 881 882 1009 1011
114 75 242 93 370 186 498 601 626 710 754 866 882 937 1010 1013
115 266 243 644 371 646 499 651 627 429 755 723 883 963 1011 895
116 273 244 202 372 404 500 421 628 794 756 486 884 747 1012 1006
117 517 245 592 373 227 501 792 629 252 757 908 885 505 1013 1014
118 104 246 323 374 896 502 802 630 373 758 718 886 855 1014 1017
119 162 247 392 375 594 503 611 631 605 759 813 887 924 1015 1018
120 53 248 297 376 418 504 602 632 848 760 476 888 734 1016 991
121 193 249 770 377 302 505 410 633 690 761 856 889 829 1017 1020
122 152 250 107 378 649 506 231 634 713 762 839 890 965 1018 1007
123 77 251 180 379 771 507 688 635 632 763 725 891 938 1019 1015
124 164 252 151 380 360 508 653 636 482 764 698 892 884 1020 1019
125 768 253 209 381 539 509 248 637 806 765 914 893 506 1021 1021
126 268 254 284 382 111 510 369 638 427 766 752 894 749 1022 1022
127 274 255 648 383 331 511 190 639 904 767 868 895 945 1023 1023
Sequence Q12, having a sequence length of 512:
[0, 1, 2, 4, 8, 16, 32, 3, 5, 64, 9, 6, 17, 10, 18, 128, 12, 33, 65, 20, 256, 34, 24, 36, 7, 129, 66, 11, 40, 68, 130, 19, 13, 48, 14, 72, 257, 21, 132, 35, 258, 26, 80, 37, 25, 22, 136, 260, 264, 38, 96, 67, 41, 144, 28, 69, 42, 49, 74, 272, 160, 288, 192, 70, 44, 131, 81, 50, 73, 15, 320, 133, 52, 23, 134, 384, 76, 137, 82, 56, 27, 97, 39, 259, 84, 138, 145, 261, 29, 43, 98, 88, 140, 30, 146, 71, 262, 265, 161, 45, 100, 51, 148, 46, 75, 266, 273, 104, 162, 53, 193, 152, 77, 164, 268, 274, 54, 83, 57, 112, 135, 78, 289, 194, 85, 276, 58, 168, 139, 99, 86, 60, 280, 89, 290, 196, 141, 101, 147, 176, 142, 321, 31, 200, 90, 292, 322, 263, 149, 102, 105, 304, 296, 163, 92, 47, 267, 385, 324, 208, 386, 150, 153, 165, 106, 55, 328, 113, 154, 79, 269, 108, 224, 166, 195, 270, 275, 291, 59, 169, 114, 277, 156, 87, 197, 116, 170, 61, 281, 278, 177, 293, 388, 91, 198, 172, 120, 201, 336, 62, 282, 143, 103, 178, 294, 93, 202, 323, 392, 297, 107, 180, 151, 209, 284, 94, 204, 298, 400, 352, 325, 155, 210, 305, 300, 109, 184, 115, 167, 225, 326, 306, 157, 329, 110, 117, 212, 171, 330, 226, 387, 308, 216, 416, 271, 279, 158, 337, 118, 332, 389, 173, 121, 199, 179, 228, 338, 312, 390, 174, 393, 283, 122, 448, 353, 203, 63, 340, 394, 181, 295, 285, 232, 124, 205, 182, 286, 299, 354, 211, 401, 185, 396, 344, 240, 206, 95, 327, 402, 356, 307, 301, 417, 213, 186, 404, 227, 418, 302, 360, 111, 331, 214, 309, 188, 449, 217, 408, 229, 159, 420, 310, 333, 119, 339, 218, 368, 230, 391, 313, 450, 334, 233, 175, 123, 341, 220, 314, 424, 395, 355, 287, 183, 234, 125, 342, 316, 241, 345, 452, 397, 403, 207, 432, 357, 187, 236, 126, 242, 398, 346, 456, 358, 405, 303, 244, 189, 361, 215, 348, 419, 406, 464, 362, 409, 219, 311, 421, 410, 231, 248, 369, 190, 364, 335, 480, 315, 221, 370, 422, 425, 451, 235, 412, 343, 372, 317, 222, 426, 453, 237, 433, 347, 243, 454, 318, 376, 428, 238, 359, 457, 399, 434, 349, 245, 458, 363, 127, 191, 407, 436, 465, 246, 350, 460, 249, 411, 365, 440, 374, 423, 466, 250, 371, 481, 413, 366, 468, 429, 252, 373, 482, 427, 414, 223, 472, 455, 377, 435, 319, 484, 430, 488, 239, 378, 459, 437, 380, 461, 496, 351, 467, 438, 251, 462, 442, 441, 469, 247, 367, 253, 375, 444, 470, 483, 415, 485, 473, 474, 254, 379, 431, 489, 486, 476, 439, 490, 463, 381, 497, 492, 443, 382, 498, 445, 471, 500, 446, 475, 487, 504, 255, 477, 491, 478, 383, 493, 499, 502, 494, 501, 447, 505, 506, 479, 508, 495, 503, 507, 509, 510, 511]
TABLE Q12
having a sequence length of 512:
Reliability or sequence Polarized channel
number of reliability sequence number
0 0
1 1
2 2
3 4
4 8
5 16
6 32
7 3
8 5
9 64
10 9
11 6
12 17
13 10
14 18
15 128
16 12
17 33
18 65
19 20
20 256
21 34
22 24
23 36
24 7
25 129
26 66
27 11
28 40
29 68
30 130
31 19
32 13
33 48
34 14
35 72
36 257
37 21
38 132
39 35
40 258
41 26
42 80
43 37
44 25
45 22
46 136
47 260
48 264
49 38
50 96
51 67
52 41
53 144
54 28
55 69
56 42
57 49
58 74
59 272
60 160
61 288
62 192
63 70
64 44
65 131
66 81
67 50
68 73
69 15
70 320
71 133
72 52
73 23
74 134
75 384
76 76
77 137
78 82
79 56
80 27
81 97
82 39
83 259
84 84
85 138
86 145
87 261
88 29
89 43
90 98
91 88
92 140
93 30
94 146
95 71
96 262
97 265
98 161
99 45
100 100
101 51
102 148
103 46
104 75
105 266
106 273
107 104
108 162
109 53
110 193
111 152
112 77
113 164
114 268
115 274
116 54
117 83
118 57
119 112
120 135
121 78
122 289
123 194
124 85
125 276
126 58
127 168
128 139
129 99
130 86
131 60
132 280
133 89
134 290
135 196
136 141
137 101
138 147
139 176
140 142
141 321
142 31
143 200
144 90
145 292
146 322
147 263
148 149
149 102
150 105
151 304
152 296
153 163
154 92
155 47
156 267
157 385
158 324
159 208
160 386
161 150
162 153
163 165
164 106
165 55
166 328
167 113
168 154
169 79
170 269
171 108
172 224
173 166
174 195
175 270
176 275
177 291
178 59
179 169
180 114
181 277
182 156
183 87
184 197
185 116
186 170
187 61
188 281
189 278
190 177
191 293
192 388
193 91
194 198
195 172
196 120
197 201
198 336
199 62
200 282
201 143
202 103
203 178
204 294
205 93
206 202
207 323
208 392
209 297
210 107
211 180
212 151
213 209
214 284
215 94
216 204
217 298
218 400
219 352
220 325
221 155
222 210
223 305
224 300
225 109
226 184
227 115
228 167
229 225
230 326
231 306
232 157
233 329
234 110
235 117
236 212
237 171
238 330
239 226
240 387
241 308
242 216
243 416
244 271
245 279
246 158
247 337
248 118
249 332
250 389
251 173
252 121
253 199
254 179
255 228
256 338
257 312
258 390
259 174
260 393
261 283
262 122
263 448
264 353
265 203
266 63
267 340
268 394
269 181
270 295
271 285
272 232
273 124
274 205
275 182
276 286
277 299
278 354
279 211
280 401
281 185
282 396
283 344
284 240
285 206
286 95
287 327
288 402
289 356
290 307
291 301
292 417
293 213
294 186
295 404
296 227
297 418
298 302
299 360
300 111
301 331
302 214
303 309
304 188
305 449
306 217
307 408
308 229
309 159
310 420
311 310
312 333
313 119
314 339
315 218
316 368
317 230
318 391
319 313
320 450
321 334
322 233
323 175
324 123
325 341
326 220
327 314
328 424
329 395
330 355
331 287
332 183
333 234
334 125
335 342
336 316
337 241
338 345
339 452
340 397
341 403
342 207
343 432
344 357
345 187
346 236
347 126
348 242
349 398
350 346
351 456
352 358
353 405
354 303
355 244
356 189
357 361
358 215
359 348
360 419
361 406
362 464
363 362
364 409
365 219
366 311
367 421
368 410
369 231
370 248
371 369
372 190
373 364
374 335
375 480
376 315
377 221
378 370
379 422
380 425
381 451
382 235
383 412
384 343
385 372
386 317
387 222
388 426
389 453
390 237
391 433
392 347
393 243
394 454
395 318
396 376
397 428
398 238
399 359
400 457
401 399
402 434
403 349
404 245
405 458
406 363
407 127
408 191
409 407
410 436
411 465
412 246
413 350
414 460
415 249
416 411
417 365
418 440
419 374
420 423
421 466
422 250
423 371
424 481
425 413
426 366
427 468
428 429
429 252
430 373
431 482
432 427
433 414
434 223
435 472
436 455
437 377
438 435
439 319
440 484
441 430
442 488
443 239
444 378
445 459
446 437
447 380
448 461
449 496
450 351
451 467
452 438
453 251
454 462
455 442
456 441
457 469
458 247
459 367
460 253
461 375
462 444
463 470
464 483
465 415
466 485
467 473
468 474
469 254
470 379
471 431
472 489
473 486
474 476
475 439
476 490
477 463
478 381
479 497
480 492
481 443
482 382
483 498
484 445
485 471
486 500
487 446
488 475
489 487
490 504
491 255
492 477
493 491
494 478
495 383
496 493
497 499
498 502
499 494
500 501
501 447
502 505
503 506
504 479
505 508
506 495
507 503
508 507
509 509
510 510
511 511
Sequence Q13, having a sequence length of 256:
[0, 1, 2, 4, 8, 16, 32, 3, 5, 64, 9, 6, 17, 10, 18, 128, 12, 33, 65, 20, 34, 24, 36, 7, 129, 66, 11, 40, 68, 130, 19, 13, 48, 14, 72, 21, 132, 35, 26, 80, 37, 25, 22, 136, 38, 96, 67, 41, 144, 28, 69, 42, 49, 74, 160, 192, 70, 44, 131, 81, 50, 73, 15, 133, 52, 23, 134, 76, 137, 82, 56, 27, 97, 39, 84, 138, 145, 29, 43, 98, 88, 140, 30, 146, 71, 161, 45, 100, 51, 148, 46, 75, 104, 162, 53, 193, 152, 77, 164, 54, 83, 57, 112, 135, 78, 194, 85, 58, 168, 139, 99, 86, 60, 89, 196, 141, 101, 147, 176, 142, 31, 200, 90, 149, 102, 105, 163, 92, 47, 208, 150, 153, 165, 106, 55, 113, 154, 79, 108, 224, 166, 195, 59, 169, 114, 156, 87, 197, 116, 170, 61, 177, 91, 198, 172, 120, 201, 62, 143, 103, 178, 93, 202, 107, 180, 151, 209, 94, 204, 155, 210, 109, 184, 115, 167, 225, 157, 110, 117, 212, 171, 226, 216, 158, 118, 173, 121, 199, 179, 228, 174, 122, 203, 63, 181, 232, 124, 205, 182, 211, 185, 240, 206, 95, 213, 186, 227, 111, 214, 188, 217, 229, 159, 119, 218, 230, 233, 175, 123, 220, 183, 234, 125, 241, 207, 187, 236, 126, 242, 244, 189, 215, 219, 231, 248, 190, 221, 235, 222, 237, 243, 238, 245, 127, 191, 246, 249, 250, 252, 223, 239, 251, 247, 253, 254, 255]
TABLE Q13
having a sequence length of 256:
Reliability or sequence Polarized channel
number of reliability sequence number
0 0
1 1
2 2
3 4
4 8
5 16
6 32
7 3
8 5
9 64
10 9
11 6
12 17
13 10
14 18
15 128
16 12
17 33
18 65
19 20
20 34
21 24
22 36
23 7
24 129
25 66
26 11
27 40
28 68
29 130
30 19
31 13
32 48
33 14
34 72
35 21
36 132
37 35
38 26
39 80
40 37
41 25
42 22
43 136
44 38
45 96
46 67
47 41
48 144
49 28
50 69
51 42
52 49
53 74
54 160
55 192
56 70
57 44
58 131
59 81
60 50
61 73
62 15
63 133
64 52
65 23
66 134
67 76
68 137
69 82
70 56
71 27
72 97
73 39
74 84
75 138
76 145
77 29
78 43
79 98
80 88
81 140
82 30
83 146
84 71
85 161
86 45
87 100
88 51
89 148
90 46
91 75
92 104
93 162
94 53
95 193
96 152
97 77
98 164
99 54
100 83
101 57
102 112
103 135
104 78
105 194
106 85
107 58
108 168
109 139
110 99
111 86
112 60
113 89
114 196
115 141
116 101
117 147
118 176
119 142
120 31
121 200
122 90
123 149
124 102
125 105
126 163
127 92
128 47
129 208
130 150
131 153
132 165
133 106
134 55
135 113
136 154
137 79
138 108
139 224
140 166
141 195
142 59
143 169
144 114
145 156
146 87
147 197
148 116
149 170
150 61
151 177
152 91
153 198
154 172
155 120
156 201
157 62
158 143
159 103
160 178
161 93
162 202
163 107
164 180
165 151
166 209
167 94
168 204
169 155
170 210
171 109
172 184
173 115
174 167
175 225
176 157
177 110
178 117
179 212
180 171
181 226
182 216
183 158
184 118
185 173
186 121
187 199
188 179
189 228
190 174
191 122
192 203
193 63
194 181
195 232
196 124
197 205
198 182
199 211
200 185
201 240
202 206
203 95
204 213
205 186
206 227
207 111
208 214
209 188
210 217
211 229
212 159
213 119
214 218
215 230
216 233
217 175
218 123
219 220
220 183
221 234
222 125
223 241
224 207
225 187
226 236
227 126
228 242
229 244
230 189
231 215
232 219
233 231
234 248
235 190
236 221
237 235
238 222
239 237
240 243
241 238
242 245
243 127
244 191
245 246
246 249
247 250
248 252
249 223
250 239
251 251
252 247
253 253
254 254
255 255
Sequence Q14, having a sequence length of 128:
[0, 1, 2, 4, 8, 16, 32, 3, 5, 64, 9, 6, 17, 10, 18, 12, 33, 65, 20, 34, 24, 36, 7, 66, 11, 40, 68, 19, 13, 48, 14, 72, 21, 35, 26, 80, 37, 25, 22, 38, 96, 67, 41, 28, 69, 42, 49, 74, 70, 44, 81, 50, 73, 15, 52, 23, 76, 82, 56, 27, 97, 39, 84, 29, 43, 98, 88, 30, 71, 45, 100, 51, 46, 75, 104, 53, 77, 54, 83, 57, 112, 78, 85, 58, 99, 86, 60, 89, 101, 31, 90, 102, 105, 92, 47, 106, 55, 113, 79, 108, 59, 114, 87, 116, 61, 91, 120, 62, 103, 93, 107, 94, 109, 115, 110, 117, 118, 121, 122, 63, 124, 95, 111, 119, 123, 125, 126, 127]
TABLE Q14
having a sequence length of 128:
Reliability or sequence Polarized channel
number of reliability sequence number
0 0
1 1
2 2
3 4
4 8
5 16
6 32
7 3
8 5
9 64
10 9
11 6
12 17
13 10
14 18
15 12
16 33
17 65
18 20
19 34
20 24
21 36
22 7
23 66
24 11
25 40
26 68
27 19
28 13
29 48
30 14
31 72
32 21
33 35
34 26
35 80
36 37
37 25
38 22
39 38
40 96
41 67
42 41
43 28
44 69
45 42
46 49
47 74
48 70
49 44
50 81
51 50
52 73
53 15
54 52
55 23
56 76
57 82
58 56
59 27
60 97
61 39
62 84
63 29
64 43
65 98
66 88
67 30
68 71
69 45
70 100
71 51
72 46
73 75
74 104
75 53
76 77
77 54
78 83
79 57
80 112
81 78
82 85
83 58
84 99
85 86
86 60
87 89
88 101
89 31
90 90
91 102
92 105
93 92
94 47
95 106
96 55
97 113
98 79
99 108
100 59
101 114
102 87
103 116
104 61
105 91
106 120
107 62
108 103
109 93
110 107
111 94
112 109
113 115
114 110
115 117
116 118
117 121
118 122
119 63
120 124
121 95
122 111
123 119
124 123
125 125
126 126
127 127
Sequence Q15, having a sequence length of 64:
[0, 1, 2, 4, 8, 16, 32, 3, 5, 9, 6, 17, 10, 18, 12, 33, 20, 34, 24, 36, 7, 11, 40, 19, 13, 48, 14, 21, 35, 26, 37, 25, 22, 38, 41, 28, 42, 49, 44, 50, 15, 52, 23, 56, 27, 39, 29, 43, 30, 45, 51, 46, 53, 54, 57, 58, 60, 31, 47, 55, 59, 61, 62, 63]
TABLE Q15
having a sequence length of 64:
Reliability or sequence Polarized channel
number of reliability sequence number
0 0
1 1
2 2
3 4
4 8
5 16
6 32
7 3
8 5
9 9
10 6
11 17
12 10
13 18
14 12
15 33
16 20
17 34
18 24
19 36
20 7
21 11
22 40
23 19
24 13
25 48
26 14
27 21
28 35
29 26
30 37
31 25
32 22
33 38
34 41
35 28
36 42
37 49
38 44
39 50
40 15
41 52
42 23
43 56
44 27
45 39
46 29
47 43
48 30
49 45
50 51
51 46
52 53
53 54
54 57
55 58
56 60
57 31
58 47
59 55
60 59
61 61
62 62
63 63
Sequence Z11, having a sequence length of 1024:
[0, 1, 2, 7, 3, 8, 11, 24, 4, 10, 13, 28, 16, 33, 35, 76, 5, 12, 14, 32, 19, 38, 47, 80, 22, 46, 42, 87, 57, 95, 101, 160, 6, 17, 21, 40, 23, 45, 51, 89, 29, 55, 59, 96, 71, 108, 113, 175, 34, 61, 74, 111, 79, 120, 129, 186, 86, 131, 141, 208, 146, 218, 236, 327, 9, 18, 26, 54, 30, 58, 70, 103, 36, 75, 62, 114, 83, 123, 135, 193, 44, 73, 85, 130, 91, 138, 145, 214, 99, 148, 162, 228, 174, 242, 256, 357, 53, 88, 97, 144, 109, 154, 169, 239, 118, 170, 185, 250, 195, 269, 282, 382, 133, 191, 211, 273, 216, 283, 301, 403, 233, 307, 322, 419, 337, 434, 460, 582, 15, 25, 31, 72, 39, 78, 81, 134, 48, 84, 92, 143, 100, 153, 157, 238, 56, 93, 102, 155, 112, 168, 182, 252, 122, 183, 192, 264, 213, 279, 297, 395, 64, 106, 119, 173, 124, 184, 198, 274, 142, 209, 217, 285, 232, 306, 317, 418, 156, 225, 240, 311, 251, 333, 339, 432, 270, 348, 370, 453, 386, 472, 511, 583, 68, 121, 137, 201, 152, 215, 231, 309, 161, 234, 244, 326, 257, 338, 356, 447, 180, 253, 265, 346, 284, 366, 384, 478, 293, 388, 406, 494, 424, 518, 532, 641, 197, 275, 288, 373, 312, 394, 409, 506, 336, 415, 433, 526, 454, 535, 567, 671, 355, 440, 461, 552, 470, 577, 591, 695, 509, 598, 613, 690, 629, 714, 743, 830, 20, 37, 41, 90, 49, 94, 104, 167, 50, 105, 115, 176, 126, 194, 202, 295, 63, 116, 127, 205, 139, 212, 223, 296, 147, 222, 237, 321, 254, 335, 342, 431, 66, 136, 149, 207, 164, 226, 241, 334, 172, 248, 258, 344, 268, 364, 377, 468, 171, 266, 277, 363, 292, 385, 397, 495, 314, 411, 425, 517, 439, 531, 555, 663, 77, 159, 165, 246, 179, 262, 276, 358, 187, 281, 287, 383, 302, 402, 414, 515, 235, 298, 313, 405, 328, 422, 438, 528, 350, 443, 464, 550, 481, 576, 593, 686, 261, 324, 345, 430, 362, 452, 466, 568, 380, 475, 487, 581, 512, 605, 619, 707, 407, 510, 519, 614, 529, 630, 609, 721, 560, 660, 672, 749, 677, 779, 794, 846, 82, 177, 181, 291, 227, 305, 316, 410, 247, 320, 329, 427, 349, 445, 463, 570, 259, 347, 361, 446, 372, 467, 483, 585, 389, 489, 505, 601, 527, 617, 640, 725, 294, 365, 376, 482, 396, 500, 521, 610, 426, 522, 533, 638, 561, 627, 667, 751, 451, 546, 574, 661, 586, 676, 688, 770, 606, 693, 692, 790, 722, 801, 813, 877, 323, 387, 412, 523, 444, 534, 554, 647, 465, 569, 578, 673, 597, 679, 691, 777, 484, 589, 611, 687, 620, 694, 723, 802, 646, 729, 740, 816, 760, 834, 844, 905, 516, 615, 636, 724, 666, 726, 756, 821, 670, 753, 772, 840, 786, 853, 870, 924, 680, 780, 798, 859, 808, 873, 865, 930, 828, 885, 893, 946, 909, 954, 963, 984, 27, 43, 52, 98, 60, 117, 128, 199, 65, 132, 140, 204, 151, 220, 224, 330, 67, 150, 158, 219, 166, 263, 271, 354, 188, 272, 290, 381, 304, 398, 413, 525, 69, 163, 178, 267, 190, 289, 299, 392, 200, 308, 318, 416, 332, 435, 449, 536, 210, 325, 341, 442, 359, 462, 473, 564, 367, 469, 490, 588, 493, 600, 616, 745, 107, 189, 196, 303, 206, 319, 331, 429, 229, 343, 351, 457, 369, 477, 488, 572, 245, 353, 375, 471, 391, 492, 497, 594, 404, 498, 504, 618, 545, 631, 656, 752, 260, 390, 400, 503, 421, 520, 524, 624, 437, 544, 557, 645, 580, 664, 674, 773, 456, 566, 587, 675, 607, 685, 709, 787, 635, 712, 730, 803, 741, 819, 836, 903, 110, 203, 221, 340, 243, 352, 371, 480, 255, 378, 393, 499, 408, 508, 513, 621, 280, 401, 420, 514, 436, 541, 553, 642, 455, 562, 579, 669, 595, 681, 700, 774, 300, 428, 448, 556, 474, 575, 573, 682, 485, 590, 599, 696, 625, 710, 718, 805, 507, 608, 633, 715, 643, 735, 742, 822, 659, 750, 764, 841, 789, 855, 871, 925, 315, 459, 476, 592, 496, 604, 626, 713, 539, 634, 650, 738, 653, 744, 758, 833, 547, 651, 658, 755, 683, 763, 783, 852, 704, 788, 797, 860, 812, 878, 888, 933, 563, 689, 698, 775, 719, 791, 800, 867, 731, 810, 823, 884, 837, 894, 907, 949, 766, 825, 842, 897, 857, 911, 916, 961, 868, 921, 929, 966, 940, 974, 983, 1003, 125, 230, 249, 379, 278, 399, 417, 530, 286, 423, 441, 543, 458, 559, 584, 701, 310, 450, 479, 571, 491, 603, 596, 706, 501, 612, 628, 728, 648, 736, 747, 829, 360, 486, 502, 602, 538, 623, 637, 739, 542, 649, 655, 748, 665, 759, 769, 848, 548, 662, 678, 768, 703, 782, 795, 861, 716, 807, 811, 879, 824, 889, 900, 944, 368, 537, 540, 644, 549, 652, 668, 762, 565, 684, 697, 778, 711, 792, 809, 875, 632, 702, 720, 796, 732, 817, 826, 886, 761, 827, 843, 898, 858, 910, 915, 960, 654, 734, 754, 818, 767, 839, 850, 902, 785, 854, 863, 914, 874, 922, 932, 969, 799, 869, 881, 928, 892, 935, 943, 976, 904, 947, 953, 981, 958, 989, 991, 1011, 374, 551, 558, 699, 622, 708, 717, 806, 639, 727, 737, 820, 757, 832, 847, 901, 657, 746, 765, 835, 776, 851, 864, 913, 793, 872, 862, 919, 887, 931, 939, 972, 705, 771, 781, 856, 804, 866, 880, 926, 815, 882, 891, 936, 899, 941, 950, 980, 838, 895, 906, 945, 917, 955, 959, 987, 923, 965, 968, 993, 975, 996, 998, 1008, 733, 784, 814, 883, 831, 890, 896, 942, 845, 908, 912, 952, 920, 956, 967, 990, 849, 918, 927, 964, 938, 970, 971, 997, 948, 977, 979, 999, 985, 1004, 1006, 1016, 876, 934, 937, 973, 951, 978, 982, 1001, 957, 986, 988, 1005, 994, 1007, 1012, 1018, 962, 992, 995, 1009, 1000, 1010, 1013, 1019, 1002, 1014, 1015, 1020, 1017, 1021, 1022, 1023]
TABLE Z11
having a sequence length of 1024:
Polarized channel Reliability or sequence
sequence number number of reliability
0 0
1 1
2 2
3 7
4 3
5 8
6 11
7 24
8 4
9 10
10 13
11 28
12 16
13 33
14 35
15 76
16 5
17 12
18 14
19 32
20 19
21 38
22 47
23 80
24 22
25 46
26 42
27 87
28 57
29 95
30 101
31 160
32 6
33 17
34 21
35 40
36 23
37 45
38 51
39 89
40 29
41 55
42 59
43 96
44 71
45 108
46 113
47 175
48 34
49 61
50 74
51 111
52 79
53 120
54 129
55 186
56 86
57 131
58 141
59 208
60 146
61 218
62 236
63 327
64 9
65 18
66 26
67 54
68 30
69 58
70 70
71 103
72 36
73 75
74 62
75 114
76 83
77 123
78 135
79 193
80 44
81 73
82 85
83 130
84 91
85 138
86 145
87 214
88 99
89 148
90 162
91 228
92 174
93 242
94 256
95 357
96 53
97 88
98 97
99 144
100 109
101 154
102 169
103 239
104 118
105 170
106 185
107 250
108 195
109 269
110 282
111 382
112 133
113 191
114 211
115 273
116 216
117 283
118 301
119 403
120 233
121 307
122 322
123 419
124 337
125 434
126 460
127 582
128 15
129 25
130 31
131 72
132 39
133 78
134 81
135 134
136 48
137 84
138 92
139 143
140 100
141 153
142 157
143 238
144 56
145 93
146 102
147 155
148 112
149 168
150 182
151 252
152 122
153 183
154 192
155 264
156 213
157 279
158 297
159 395
160 64
161 106
162 119
163 173
164 124
165 184
166 198
167 274
168 142
169 209
170 217
171 285
172 232
173 306
174 317
175 418
176 156
177 225
178 240
179 311
180 251
181 333
182 339
183 432
184 270
185 348
186 370
187 453
188 386
189 472
190 511
191 583
192 68
193 121
194 137
195 201
196 152
197 215
198 231
199 309
200 161
201 234
202 244
203 326
204 257
205 338
206 356
207 447
208 180
209 253
210 265
211 346
212 284
213 366
214 384
215 478
216 293
217 388
218 406
219 494
220 424
221 518
222 532
223 641
224 197
225 275
226 288
227 373
228 312
229 394
230 409
231 506
232 336
233 415
234 433
235 526
236 454
237 535
238 567
239 671
240 355
241 440
242 461
243 552
244 470
245 577
246 591
247 695
248 509
249 598
250 613
251 690
252 629
253 714
254 743
255 830
256 20
257 37
258 41
259 90
260 49
261 94
262 104
263 167
264 50
265 105
266 115
267 176
268 126
269 194
270 202
271 295
272 63
273 116
274 127
275 205
276 139
277 212
278 223
279 2%
280 147
281 222
282 237
283 321
284 254
285 335
286 342
287 431
288 66
289 136
290 149
291 207
292 164
293 226
294 241
295 334
296 172
297 248
298 258
299 344
300 268
301 364
302 377
303 468
304 171
305 266
306 277
307 363
308 292
309 385
310 397
311 495
312 314
313 411
314 425
315 517
316 439
317 531
318 555
319 663
320 77
321 159
322 165
323 246
324 179
325 262
326 276
327 358
328 187
329 281
330 287
331 383
332 302
333 402
334 414
335 515
336 235
337 298
338 313
339 405
340 328
341 422
342 438
343 528
344 350
345 443
346 464
347 550
348 481
349 576
350 593
351 686
352 261
353 324
354 345
355 430
356 362
357 452
358 466
359 568
360 380
361 475
362 487
363 581
364 512
365 605
366 619
367 707
368 407
369 510
370 519
371 614
372 529
373 630
374 609
375 721
376 560
377 660
378 672
379 749
380 677
381 779
382 794
383 846
384 82
385 177
386 181
387 291
388 227
389 305
390 316
391 410
392 247
393 320
394 329
395 427
396 349
397 445
398 463
399 570
400 259
401 347
402 361
403 446
404 372
405 467
406 483
407 585
408 389
409 489
410 505
411 601
412 527
413 617
414 640
415 725
416 294
417 365
418 376
419 482
420 396
421 500
422 521
423 610
424 426
425 522
426 533
427 638
428 561
429 627
430 667
431 751
432 451
433 546
434 574
435 661
436 586
437 676
438 688
439 770
440 606
441 693
442 692
443 790
444 722
445 801
446 813
447 877
448 323
449 387
450 412
451 523
452 444
453 534
454 554
455 647
456 465
457 569
458 578
459 673
460 597
461 679
462 691
463 777
464 484
465 589
466 611
467 687
468 620
469 694
470 723
471 802
472 646
473 729
474 740
475 816
476 760
477 834
478 844
479 905
480 516
481 615
482 636
483 724
484 666
485 726
486 756
487 821
488 670
489 753
490 772
491 840
492 786
493 853
494 870
495 924
496 680
497 780
498 798
499 859
500 808
501 873
502 865
503 930
504 828
505 885
506 893
507 946
508 909
509 954
510 963
511 984
512 27
513 43
514 52
515 98
516 60
517 117
518 128
519 199
520 65
521 132
522 140
523 204
524 151
525 220
526 224
527 330
528 67
529 150
530 158
531 219
532 166
533 263
534 271
535 354
536 188
537 272
538 290
539 381
540 304
541 398
542 413
543 525
544 69
545 163
546 178
547 267
548 190
549 289
550 299
551 392
552 200
553 308
554 318
555 416
556 332
557 435
558 449
559 536
560 210
561 325
562 341
563 442
564 359
565 462
566 473
567 564
568 367
569 469
570 490
571 588
572 493
573 600
574 616
575 745
576 107
577 189
578 196
579 303
580 206
581 319
582 331
583 429
584 229
585 343
586 351
587 457
588 369
589 477
590 488
591 572
592 245
593 353
594 375
595 471
596 391
597 492
598 497
599 594
600 404
601 498
602 504
603 618
604 545
605 631
606 656
607 752
608 260
609 390
610 400
611 503
612 421
613 520
614 524
615 624
616 437
617 544
618 557
619 645
620 580
621 664
622 674
623 773
624 456
625 566
626 587
627 675
628 607
629 685
630 709
631 787
632 635
633 712
634 730
635 803
636 741
637 819
638 836
639 903
640 110
641 203
642 221
643 340
644 243
645 352
646 371
647 480
648 255
649 378
650 393
651 499
652 408
653 508
654 513
655 621
656 280
657 401
658 420
659 514
660 436
661 541
662 553
663 642
664 455
665 562
666 579
667 669
668 595
669 681
670 700
671 774
672 300
673 428
674 448
675 556
676 474
677 575
678 573
679 682
680 485
681 590
682 599
683 696
684 625
685 710
686 718
687 805
688 507
689 608
690 633
691 715
692 643
693 735
694 742
695 822
696 659
697 750
698 764
699 841
700 789
701 855
702 871
703 925
704 315
705 459
706 476
707 592
708 496
709 604
710 626
711 713
712 539
713 634
714 650
715 738
716 653
717 744
718 758
719 833
720 547
721 651
722 658
723 755
724 683
725 763
726 783
727 852
728 704
729 788
730 797
731 860
732 812
733 878
734 888
735 933
736 563
737 689
738 698
739 775
740 719
741 791
742 800
743 867
744 731
745 810
746 823
747 884
748 837
749 894
750 907
751 949
752 766
753 825
754 842
755 897
756 857
757 911
758 916
759 961
760 868
761 921
762 929
763 966
764 940
765 974
766 983
767 1003
768 125
769 230
770 249
771 379
772 278
773 399
774 417
775 530
776 286
777 423
778 441
779 543
780 458
781 559
782 584
783 701
784 310
785 450
786 479
787 571
788 491
789 603
790 596
791 706
792 501
793 612
794 628
795 728
796 648
797 736
798 747
799 829
800 360
801 486
802 502
803 602
804 538
805 623
806 637
807 739
808 542
809 649
810 655
811 748
812 665
813 759
814 769
815 848
816 548
817 662
818 678
819 768
820 703
821 782
822 795
823 861
824 716
825 807
826 811
827 879
828 824
829 889
830 900
831 944
832 368
833 537
834 540
835 644
836 549
837 652
838 668
839 762
840 565
841 684
842 697
843 778
844 711
845 792
846 809
847 875
848 632
849 702
850 720
851 796
852 732
853 817
854 826
855 886
856 761
857 827
858 843
859 898
860 858
861 910
862 915
863 960
864 654
865 734
866 754
867 818
868 767
869 839
870 850
871 902
872 785
873 854
874 863
875 914
876 874
877 922
878 932
879 969
880 799
881 869
882 881
883 928
884 892
885 935
886 943
887 976
888 904
889 947
890 953
891 981
892 958
893 989
894 991
895 1011
896 374
897 551
898 558
899 699
900 622
901 708
902 717
903 806
904 639
905 727
906 737
907 820
908 757
909 832
910 847
911 901
912 657
913 746
914 765
915 835
916 776
917 851
918 864
919 913
920 793
921 872
922 862
923 919
924 887
925 931
926 939
927 972
928 705
929 771
930 781
931 856
932 804
933 866
934 880
935 926
936 815
937 882
938 891
939 936
940 899
941 941
942 950
943 980
944 838
945 895
946 906
947 945
948 917
949 955
950 959
951 987
952 923
953 965
954 968
955 993
956 975
957 996
958 998
959 1008
960 733
961 784
962 814
963 883
964 831
965 890
966 896
967 942
968 845
969 908
970 912
971 952
972 920
973 956
974 967
975 990
976 849
977 918
978 927
979 964
980 938
981 970
982 971
983 997
984 948
985 977
986 979
987 999
988 985
989 1004
990 1006
991 1016
992 876
993 934
994 937
995 973
996 951
997 978
998 982
999 1001
1000 957
1001 986
1002 988
1003 1005
1004 994
1005 1007
1006 1012
1007 1018
1008 962
1009 992
1010 995
1011 1009
1012 1000
1013 1010
1014 1013
1015 1019
1016 1002
1017 1014
1018 1015
1019 1020
1020 1017
1021 1021
1022 1022
1023 1023
Sequence Z12, having a sequence length of 512:
[0, 1, 2, 7, 3, 8, 11, 24, 4, 10, 13, 27, 16, 32, 34, 69, 5, 12, 14, 31, 19, 37, 45, 73, 22, 44, 41, 80, 54, 88, 93, 142, 6, 17, 21, 39, 23, 43, 49, 82, 28, 52, 56, 89, 64, 99, 103, 155, 33, 57, 67, 101, 72, 109, 116, 165, 79, 118, 126, 178, 131, 187, 199, 266, 9, 18, 26, 51, 29, 55, 63, 95, 35, 68, 58, 104, 76, 112, 121, 169, 42, 66, 78, 117, 84, 124, 130, 183, 91, 133, 144, 193, 154, 205, 215, 286, 50, 81, 90, 129, 100, 137, 149, 202, 107, 150, 164, 210, 171, 225, 234, 300, 119, 167, 180, 227, 185, 235, 248, 313, 196, 252, 262, 324, 273, 334, 347, 407, 15, 25, 30, 65, 38, 71, 74, 120, 46, 77, 85, 128, 92, 136, 140, 201, 53, 86, 94, 138, 102, 148, 161, 212, 111, 162, 168, 221, 182, 232, 246, 309, 60, 98, 108, 153, 113, 163, 173, 228, 127, 179, 186, 237, 195, 251, 259, 323, 139, 190, 203, 254, 211, 269, 275, 332, 226, 281, 294, 345, 304, 356, 372, 408, 62, 110, 123, 174, 135, 184, 194, 253, 143, 197, 206, 265, 216, 274, 285, 342, 159, 213, 222, 279, 236, 293, 302, 358, 242, 306, 315, 365, 326, 377, 387, 434, 172, 229, 239, 296, 255, 308, 317, 369, 272, 322, 333, 382, 346, 390, 398, 443, 284, 337, 348, 393, 355, 404, 412, 458, 370, 415, 422, 453, 429, 460, 469, 491, 20, 36, 40, 83, 47, 87, 96, 147, 48, 97, 105, 156, 114, 170, 175, 244, 59, 106, 115, 176, 125, 181, 189, 245, 132, 188, 200, 261, 214, 271, 276, 331, 61, 122, 134, 177, 145, 191, 204, 270, 152, 209, 217, 277, 224, 291, 298, 354, 151, 223, 231, 290, 241, 303, 311, 366, 257, 319, 327, 376, 336, 386, 395, 439, 70, 141, 146, 207, 158, 220, 230, 287, 166, 233, 238, 301, 249, 312, 321, 374, 198, 247, 256, 314, 267, 325, 335, 384, 283, 338, 350, 392, 359, 403, 413, 450, 219, 264, 278, 330, 289, 344, 352, 399, 299, 357, 363, 406, 373, 417, 426, 459, 316, 371, 378, 423, 385, 430, 419, 461, 396, 437, 444, 470, 447, 478, 482, 495, 75, 157, 160, 240, 192, 250, 258, 318, 208, 260, 268, 329, 282, 340, 349, 401, 218, 280, 288, 341, 295, 353, 361, 409, 307, 364, 368, 416, 383, 425, 433, 465, 243, 292, 297, 360, 310, 367, 379, 420, 328, 380, 388, 432, 397, 428, 441, 471, 343, 391, 402, 438, 410, 446, 452, 475, 418, 456, 455, 481, 462, 484, 487, 501, 263, 305, 320, 381, 339, 389, 394, 436, 351, 400, 405, 445, 414, 448, 454, 477, 362, 411, 421, 451, 427, 457, 463, 485, 435, 467, 468, 488, 474, 492, 494, 504, 375, 424, 431, 464, 440, 466, 473, 489, 442, 472, 476, 493, 480, 496, 499, 506, 449, 479, 483, 497, 486, 500, 498, 507, 490, 502, 503, 508, 505, 509, 510, 511]
TABLE Z12
having a sequence length of 512:
Polarized channel Reliability or sequence
sequence number number of reliability
0 0
1 1
2 2
3 7
4 3
5 8
6 11
7 24
8 4
9 10
10 13
11 27
12 16
13 32
14 34
15 69
16 5
17 12
18 14
19 31
20 19
21 37
22 45
23 73
24 22
25 44
26 41
27 80
28 54
29 88
30 93
31 142
32 6
33 17
34 21
35 39
36 23
37 43
38 49
39 82
40 28
41 52
42 56
43 89
44 64
45 99
46 103
47 155
48 33
49 57
50 67
51 101
52 72
53 109
54 116
55 165
56 79
57 118
58 126
59 178
60 131
61 187
62 199
63 266
64 9
65 18
66 26
67 51
68 29
69 55
70 63
71 95
72 35
73 68
74 58
75 104
76 76
77 112
78 121
79 169
80 42
81 66
82 78
83 117
84 84
85 124
86 130
87 183
88 91
89 133
90 144
91 193
92 154
93 205
94 215
95 286
96 50
97 81
98 90
99 129
100 100
101 137
102 149
103 202
104 107
105 150
106 164
107 210
108 171
109 225
110 234
111 300
112 119
113 167
114 180
115 227
116 185
117 235
118 248
119 313
120 196
121 252
122 262
123 324
124 273
125 334
126 347
127 407
128 15
129 25
130 30
131 65
132 38
133 71
134 74
135 120
136 46
137 77
138 85
139 128
140 92
141 136
142 140
143 201
144 53
145 86
146 94
147 138
148 102
149 148
150 161
151 212
152 111
153 162
154 168
155 221
156 182
157 232
158 246
159 309
160 60
161 98
162 108
163 153
164 113
165 163
166 173
167 228
168 127
169 179
170 186
171 237
172 195
173 251
174 259
175 323
176 139
177 190
178 203
179 254
180 211
181 269
182 275
183 332
184 226
185 281
186 294
187 345
188 304
189 356
190 372
191 408
192 62
193 110
194 123
195 174
196 135
197 184
198 194
199 253
200 143
201 197
202 206
203 265
204 216
205 274
206 285
207 342
208 159
209 213
210 222
211 279
212 236
213 293
214 302
215 358
216 242
217 306
218 315
219 365
220 326
221 377
222 387
223 434
224 172
225 229
226 239
227 296
228 255
229 308
230 317
231 369
232 272
233 322
234 333
235 382
236 346
237 390
238 398
239 443
240 284
241 337
242 348
243 393
244 355
245 404
246 412
247 458
248 370
249 415
250 422
251 453
252 429
253 460
254 469
255 491
256 20
257 36
258 40
259 83
260 47
261 87
262 96
263 147
264 48
265 97
266 105
267 156
268 114
269 170
270 175
271 244
272 59
273 106
274 115
275 176
276 125
277 181
278 189
279 245
280 132
281 188
282 200
283 261
284 214
285 271
286 276
287 331
288 61
289 122
290 134
291 177
292 145
293 191
294 204
295 270
296 152
297 209
298 217
299 277
300 224
301 291
302 298
303 354
304 151
305 223
306 231
307 290
308 241
309 303
310 311
311 366
312 257
313 319
314 327
315 376
316 336
317 386
318 395
319 439
320 70
321 141
322 146
323 207
324 158
325 220
326 230
327 287
328 166
329 233
330 238
331 301
332 249
333 312
334 321
335 374
336 198
337 247
338 256
339 314
340 267
341 325
342 335
343 384
344 283
345 338
346 350
347 392
348 359
349 403
350 413
351 450
352 219
353 264
354 278
355 330
356 289
357 344
358 352
359 399
360 299
361 357
362 363
363 406
364 373
365 417
366 426
367 259
368 316
369 371
370 378
371 423
372 385
373 430
374 419
375 461
376 396
377 437
378 444
379 470
380 447
381 478
382 482
383 495
384 75
385 157
386 160
387 240
388 192
389 250
390 258
391 318
392 208
393 260
394 268
395 329
396 282
397 340
398 349
399 401
400 218
401 280
402 288
403 341
404 295
405 353
406 361
407 409
408 307
409 364
410 368
411 416
412 383
413 425
414 433
415 465
416 243
417 292
418 297
419 360
420 310
421 367
422 379
423 420
424 328
425 380
426 388
427 432
428 397
429 428
430 441
431 471
432 343
433 391
434 402
435 438
436 410
437 446
438 452
439 475
440 418
441 456
442 455
443 481
444 462
445 484
446 487
447 501
448 263
449 305
450 320
451 381
452 339
453 389
454 394
455 436
456 351
457 400
458 405
459 445
460 414
461 448
462 454
463 477
464 362
465 411
466 421
467 451
468 427
469 457
470 463
471 485
472 435
473 467
474 468
475 488
476 474
477 492
478 494
479 504
480 375
481 424
482 431
483 464
484 440
485 466
486 473
487 489
488 442
489 472
490 476
491 493
492 480
493 496
494 499
495 506
496 449
497 479
498 483
499 497
500 486
501 500
502 498
503 507
504 490
505 502
506 503
507 508
508 505
509 509
510 510
511 511
Sequence Z13, having a sequence length of 256:
[0, 1, 2, 7, 3, 8, 11, 23, 4, 10, 13, 26, 16, 31, 33, 62, 5, 12, 14, 30, 19, 35, 42, 65, 21, 41, 38, 71, 49, 77, 82, 120, 6, 17, 20, 37, 22, 40, 44, 73, 27, 47, 51, 78, 57, 86, 90, 128, 32, 52, 60, 88, 64, 94, 99, 134, 70, 101, 107, 142, 112, 150, 157, 193, 9, 18, 25, 46, 28, 50, 56, 84, 34, 61, 53, 91, 67, 97, 104, 137, 39, 59, 69, 100, 74, 106, 111, 146, 80, 113, 122, 152, 127, 161, 167, 203, 45, 72, 79, 110, 87, 116, 124, 159, 92, 125, 133, 163, 138, 171, 177, 207, 102, 135, 144, 173, 148, 178, 184, 213, 155, 186, 191, 218, 196, 222, 227, 243, 15, 24, 29, 58, 36, 63, 66, 103, 43, 68, 75, 109, 81, 115, 119, 158, 48, 76, 83, 117, 89, 123, 130, 165, 96, 131, 136, 169, 145, 176, 183, 212, 54, 85, 93, 126, 98, 132, 140, 174, 108, 143, 149, 180, 154, 185, 190, 217, 118, 151, 160, 188, 164, 194, 198, 220, 172, 200, 205, 225, 209, 230, 235, 244, 55, 95, 105, 141, 114, 147, 153, 187, 121, 156, 162, 192, 168, 197, 202, 224, 129, 166, 170, 199, 179, 204, 208, 231, 182, 210, 214, 232, 219, 236, 238, 249, 139, 175, 181, 206, 189, 211, 215, 233, 195, 216, 221, 237, 226, 239, 241, 250, 201, 223, 228, 240, 229, 242, 245, 252, 234, 246, 247, 251, 248, 253, 254, 255]
TABLE Z13
having a sequence length of 256:
Polarized channel Reliability or sequence
sequence number number of reliability
0 0
1 1
2 2
3 7
4 3
5 8
6 11
7 23
8 4
9 10
10 13
11 26
12 16
13 31
14 33
15 62
16 5
17 12
18 14
19 30
20 19
21 35
22 42
23 65
24 21
25 41
26 38
27 71
28 49
29 77
30 82
31 120
32 6
33 17
34 20
35 37
36 22
37 40
38 44
39 73
40 27
41 47
42 51
43 78
44 57
45 86
46 90
47 128
48 32
49 52
50 60
51 88
52 64
53 94
54 99
55 134
56 70
57 101
58 107
59 142
60 112
61 150
62 157
63 193
64 9
65 18
66 25
67 46
68 28
69 50
70 56
71 84
72 34
73 61
74 53
75 91
76 67
77 97
78 104
79 137
80 39
81 59
82 69
83 100
84 74
85 106
86 111
87 146
88 80
89 113
90 122
91 152
92 127
93 161
94 167
95 203
96 45
97 72
98 79
99 110
100 87
101 116
102 124
103 159
104 92
105 125
106 133
107 163
108 138
109 171
110 177
111 207
112 102
113 135
114 144
115 173
116 148
117 178
118 184
119 213
120 155
121 186
122 191
123 218
124 196
125 222
126 227
127 243
128 15
129 24
130 29
131 58
132 36
133 63
134 66
135 103
136 43
137 68
138 75
139 109
140 81
141 115
142 119
143 158
144 48
145 76
146 83
147 117
148 89
149 123
150 130
151 165
152 96
153 131
154 136
155 169
156 145
157 176
158 183
159 212
160 54
161 85
162 93
163 126
164 98
165 132
166 140
167 174
168 108
169 143
170 149
171 180
172 154
173 185
174 190
175 217
176 118
177 151
178 160
179 188
180 164
181 194
182 198
183 220
184 172
185 200
186 205
187 225
188 209
189 230
190 235
191 244
192 55
193 95
194 105
195 141
196 114
197 147
198 153
199 187
200 121
201 156
202 162
203 192
204 168
205 197
206 202
207 224
208 129
209 166
210 170
211 199
212 179
213 204
214 208
215 231
216 182
217 210
218 214
219 232
220 219
221 236
222 238
223 249
224 139
225 175
226 181
227 206
228 189
229 211
230 215
231 233
232 195
233 216
234 221
235 237
236 226
237 239
238 241
239 250
240 201
241 223
242 228
243 240
244 229
245 242
246 245
247 252
248 234
249 246
250 247
251 251
252 248
253 253
254 254
255 255
Sequence Z14, having a sequence length of 128:
[0, 1, 2, 7, 3, 8, 11, 22, 4, 10, 13, 24, 15, 28, 30, 53, 5, 12, 14, 27, 18, 32, 38, 55, 20, 37, 34, 59, 43, 63, 67, 89, 6, 16, 19, 33, 21, 36, 39, 61, 25, 42, 45, 64, 49, 69, 72, 94, 29, 46, 51, 71, 54, 75, 77, 96, 58, 79, 83, 100, 86, 104, 107, 119, 9, 17, 23, 41, 26, 44, 48, 68, 31, 52, 47, 73, 56, 76, 81, 98, 35, 50, 57, 78, 62, 82, 85, 102, 66, 87, 90, 105, 93, 109, 111, 121, 40, 60, 65, 84, 70, 88, 91, 108, 74, 92, 95, 110, 99, 112, 114, 122, 80, 97, 101, 113, 103, 115, 116, 123, 106, 117, 118, 124, 120, 125, 126, 127]
TABLE Z14
having a sequence length of 128:
Polarized channel Reliability or sequence
sequence number number of reliability
0 0
1 1
2 2
3 7
4 3
5 8
6 11
7 22
8 4
9 10
10 13
11 24
12 15
13 28
14 30
15 53
16 5
17 12
18 14
19 27
20 18
21 32
22 38
23 55
24 20
25 37
26 34
27 59
28 43
29 63
30 67
31 89
32 6
33 16
34 19
35 33
36 21
37 36
38 39
39 61
40 25
41 42
42 45
43 64
44 49
45 69
46 72
47 94
48 29
49 46
50 51
51 71
52 54
53 75
54 77
55 96
56 58
57 79
58 83
59 100
60 86
61 104
62 107
63 119
64 9
65 17
66 23
67 41
68 26
69 44
70 48
71 68
72 31
73 52
74 47
75 73
76 56
77 76
78 81
79 98
80 35
81 50
82 57
83 78
84 62
85 82
86 85
87 102
88 66
89 87
90 90
91 105
92 93
93 109
94 111
95 121
96 40
97 60
98 65
99 84
100 70
101 88
102 91
103 108
104 74
105 92
106 95
107 110
108 99
109 112
110 114
111 122
112 80
113 97
114 101
115 113
116 103
117 115
118 116
119 123
120 106
121 117
122 118
123 124
124 120
125 125
126 126
127 127
Sequence Z15, having a sequence length of 64:
[0, 1, 2, 7, 3, 8, 10, 20, 4, 9, 12, 21, 14, 24, 26, 40, 5, 11, 13, 23, 16, 27, 32, 42, 18, 31, 29, 44, 35, 46, 48, 57, 6, 15, 17, 28, 19, 30, 33, 45, 22, 34, 36, 47, 38, 49, 51, 58, 25, 37, 39, 50, 41, 52, 53, 59, 43, 54, 55, 60, 56, 61, 62, 63]
TABLE Z15
having a sequence length of 64:
Polarized channel Reliability or sequence
sequence number number of reliability
0 0
1 1
2 2
3 7
4 3
5 8
6 10
7 20
8 4
9 9
10 12
11 21
12 14
13 24
14 26
15 40
16 5
17 11
18 13
19 23
20 16
21 27
22 32
23 42
24 18
25 31
26 29
27 44
28 35
29 46
30 48
31 57
32 6
33 15
34 17
35 28
36 19
37 30
38 33
39 45
40 22
41 34
42 36
43 47
44 38
45 49
46 51
47 58
48 25
49 37
50 39
51 50
52 41
53 52
54 53
55 59
56 43
57 54
58 55
59 60
60 56
61 61
62 62
63 63
Fourth group of sequences (a criterion that considers a performance balance under partial-order (partial-order) constraints).
Sequence Q16, having a sequence length of 1024:
[0, 1, 2, 4, 8, 16, 32, 3, 5, 64, 9, 6, 17, 10, 18, 128, 12, 33, 65, 20, 256, 34, 24, 36, 7, 129, 66, 512, 11, 40, 68, 130, 19, 13, 48, 14, 72, 257, 21, 132, 35, 258, 22, 80, 136, 513, 25, 37, 260, 264, 26, 96, 514, 38, 67, 41, 144, 28, 69, 516, 42, 272, 49, 70, 520, 160, 44, 131, 73, 288, 528, 192, 50, 74, 544, 52, 15, 133, 320, 81, 23, 134, 384, 76, 56, 259, 82, 137, 27, 97, 39, 84, 138, 145, 261, 29, 43, 98, 515, 88, 140, 30, 146, 71, 262, 265, 161, 576, 45, 100, 640, 51, 148, 46, 75, 266, 273, 517, 104, 162, 53, 193, 152, 77, 164, 768, 268, 274, 518, 54, 83, 57, 521, 112, 135, 78, 289, 194, 85, 276, 522, 58, 168, 139, 99, 86, 60, 280, 89, 290, 529, 524, 196, 141, 101, 147, 176, 142, 530, 321, 90, 200, 31, 545, 292, 322, 532, 263, 149, 102, 105, 296, 304, 163, 92, 47, 267, 150, 208, 385, 546, 386, 324, 106, 153, 165, 55, 328, 536, 577, 548, 113, 154, 79, 269, 108, 578, 224, 166, 519, 552, 195, 270, 641, 523, 275, 580, 291, 169, 59, 560, 114, 277, 156, 87, 197, 116, 170, 61, 531, 525, 642, 281, 278, 526, 177, 293, 388, 91, 584, 769, 198, 172, 120, 201, 336, 62, 282, 143, 103, 178, 294, 93, 644, 202, 592, 323, 392, 297, 770, 107, 180, 151, 209, 284, 648, 94, 204, 298, 400, 352, 608, 325, 533, 155, 210, 305, 547, 300, 109, 184, 115, 534, 167, 225, 537, 326, 306, 772, 157, 656, 329, 110, 117, 212, 171, 330, 226, 549, 776, 538, 387, 308, 216, 416, 271, 279, 158, 337, 550, 672, 118, 332, 579, 540, 389, 173, 121, 553, 199, 784, 179, 228, 338, 390, 122, 554, 448, 312, 581, 393, 283, 704, 174, 394, 181, 340, 203, 353, 561, 527, 582, 556, 63, 295, 285, 232, 124, 286, 562, 205, 182, 643, 585, 299, 354, 211, 401, 185, 396, 344, 586, 645, 593, 535, 240, 206, 95, 327, 564, 800, 402, 356, 307, 301, 417, 213, 186, 539, 404, 227, 594, 568, 771, 418, 649, 302, 832, 551, 111, 896, 360, 588, 609, 331, 214, 309, 188, 449, 217, 646, 408, 229, 541, 159, 420, 596, 650, 773, 310, 333, 119, 657, 658, 610, 368, 339, 391, 313, 218, 334, 542, 230, 233, 774, 612, 175, 123, 652, 600, 450, 583, 341, 220, 555, 314, 557, 424, 395, 777, 673, 355, 287, 183, 234, 125, 616, 342, 563, 778, 660, 558, 452, 674, 397, 785, 432, 316, 345, 241, 207, 403, 357, 187, 587, 565, 664, 624, 780, 236, 126, 242, 398, 705, 346, 456, 358, 405, 303, 569, 189, 595, 215, 566, 676, 361, 706, 589, 244, 786, 647, 348, 419, 406, 464, 801, 590, 362, 570, 409, 680, 597, 788, 572, 219, 311, 708, 598, 601, 651, 421, 792, 802, 611, 602, 369, 190, 688, 653, 248, 231, 410, 364, 654, 659, 335, 480, 315, 221, 613, 422, 370, 425, 235, 451, 543, 614, 412, 343, 222, 775, 317, 372, 426, 453, 237, 559, 833, 804, 712, 834, 661, 808, 779, 617, 604, 433, 720, 816, 836, 347, 897, 243, 662, 454, 318, 675, 618, 898, 781, 376, 428, 665, 736, 567, 840, 625, 238, 359, 457, 399, 787, 677, 434, 349, 458, 678, 245, 666, 363, 591, 127, 620, 407, 782, 436, 465, 626, 571, 246, 681, 350, 707, 460, 599, 668, 789, 249, 411, 682, 573, 365, 803, 790, 709, 440, 466, 793, 574, 371, 423, 689, 603, 366, 628, 250, 413, 468, 655, 481, 900, 805, 191, 373, 615, 684, 427, 710, 794, 605, 414, 252, 713, 374, 848, 690, 632, 806, 482, 429, 904, 809, 455, 223, 663, 835, 692, 619, 472, 714, 796, 721, 837, 716, 864, 810, 606, 912, 722, 696, 377, 817, 435, 484, 621, 812, 319, 430, 838, 667, 239, 378, 459, 437, 622, 627, 488, 380, 818, 461, 496, 669, 679, 724, 841, 629, 351, 467, 438, 737, 247, 462, 441, 442, 469, 251, 683, 842, 738, 899, 670, 783, 849, 820, 728, 928, 791, 367, 901, 630, 685, 844, 633, 711, 253, 691, 824, 902, 686, 740, 850, 375, 444, 470, 483, 905, 415, 485, 795, 473, 634, 744, 852, 960, 865, 693, 797, 906, 715, 807, 474, 636, 694, 254, 717, 575, 811, 697, 866, 798, 379, 431, 913, 607, 489, 723, 486, 908, 718, 813, 476, 856, 839, 725, 698, 914, 752, 868, 819, 814, 439, 929, 490, 623, 671, 739, 916, 463, 843, 381, 497, 930, 821, 726, 961, 872, 492, 631, 729, 700, 443, 741, 845, 920, 382, 822, 851, 730, 498, 880, 742, 445, 471, 635, 932, 687, 903, 825, 500, 846, 745, 826, 732, 446, 962, 936, 475, 853, 867, 637, 907, 487, 695, 746, 828, 753, 854, 857, 504, 799, 909, 719, 638, 915, 477, 255, 964, 699, 748, 869, 944, 491, 754, 910, 858, 917, 478, 968, 870, 815, 383, 727, 493, 873, 701, 931, 756, 860, 499, 731, 823, 702, 918, 921, 874, 494, 976, 760, 933, 881, 501, 743, 922, 876, 847, 934, 827, 733, 882, 502, 447, 992, 937, 963, 747, 505, 855, 924, 734, 829, 938, 884, 506, 965, 749, 945, 966, 755, 859, 940, 830, 911, 871, 888, 479, 946, 750, 969, 861, 757, 970, 919, 875, 758, 508, 862, 639, 948, 977, 923, 972, 761, 877, 952, 495, 703, 935, 978, 883, 762, 503, 925, 878, 735, 993, 885, 939, 994, 980, 926, 764, 941, 967, 886, 831, 947, 507, 889, 984, 751, 942, 996, 971, 890, 509, 949, 973, 1000, 892, 950, 863, 759, 1008, 510, 979, 953, 763, 974, 954, 879, 981, 982, 927, 995, 765, 956, 887, 985, 997, 986, 943, 891, 998, 766, 511, 988, 1001, 951, 1002, 893, 975, 894, 1009, 955, 1004, 1010, 957, 983, 958, 987, 1012, 999, 1016, 767, 989, 1003, 990, 1005, 895, 1011, 1013, 959, 1006, 1014, 1017, 1018, 991, 1020, 1007, 1015, 1019, 1021, 1022, 1023]
TABLE Q16
having a sequence length of 1024:
Reliability or sequence Polarized channel
number of reliability sequence number
0 0
1 1
2 2
3 4
4 8
5 16
6 32
7 3
8 5
9 64
10 9
11 6
12 17
13 10
14 18
15 128
16 12
17 33
18 65
19 20
20 256
21 34
22 24
23 36
24 7
25 129
26 66
27 512
28 11
29 40
30 68
31 130
32 19
33 13
34 48
35 14
36 72
37 257
38 21
39 132
40 35
41 258
42 22
43 80
44 136
45 513
46 25
47 37
48 260
49 264
50 26
51 96
52 514
53 38
54 67
55 41
56 144
57 28
58 69
59 516
60 42
61 272
62 49
63 70
64 520
65 160
66 44
67 131
68 73
69 288
70 528
71 192
72 50
73 74
75 544
75 52
76 15
77 133
78 320
79 81
80 23
81 134
82 384
83 76
84 56
85 259
86 82
87 137
88 27
89 97
90 39
91 84
92 138
93 145
94 261
95 29
96 43
97 98
98 515
99 88
100 140
101 30
102 146
103 71
104 262
105 265
106 161
107 576
108 45
109 100
110 640
111 51
112 148
113 46
114 75
115 266
116 273
117 517
118 104
119 162
120 53
121 193
122 152
123 77
124 164
125 768
126 268
127 274
128 518
129 54
130 83
131 57
132 521
133 112
134 135
135 78
136 289
137 194
138 85
139 276
140 522
141 58
142 168
143 139
144 99
145 86
146 60
147 280
148 89
149 290
150 529
151 524
152 196
153 141
154 101
155 147
156 176
157 142
158 530
159 321
160 90
161 200
162 31
163 545
164 292
165 322
166 532
167 263
168 149
169 102
170 105
171 296
172 304
173 163
174 92
175 47
176 267
177 150
178 208
179 385
180 546
181 386
182 324
183 106
184 153
185 165
186 55
187 328
188 536
189 577
190 548
191 113
192 154
193 79
194 269
195 108
196 578
197 224
198 166
199 519
200 552
201 195
202 270
203 641
204 523
205 275
206 580
207 291
208 169
209 59
210 560
211 114
212 277
213 156
214 87
215 197
216 116
217 170
218 61
219 531
220 525
221 642
222 281
223 278
224 526
225 177
226 293
227 388
228 91
229 584
230 769
231 198
232 172
233 120
234 201
235 336
236 62
237 282
238 143
239 103
240 178
241 294
242 93
243 644
244 202
245 592
246 323
247 392
248 297
249 770
250 107
251 180
252 151
253 209
254 284
255 648
256 94
257 204
258 298
259 400
260 352
261 608
262 325
263 533
264 155
265 210
266 305
267 547
268 300
269 109
270 184
271 115
272 534
273 167
274 225
275 537
276 326
277 306
278 772
279 157
280 656
281 329
282 110
283 117
284 212
285 171
286 330
287 226
288 549
289 776
290 538
291 387
292 308
293 216
294 416
295 271
296 279
297 158
298 337
299 550
300 672
301 118
302 332
303 579
304 540
305 389
306 173
307 121
308 553
309 199
310 784
311 179
312 228
313 338
314 390
315 122
316 554
317 448
318 312
319 581
320 393
321 283
322 704
323 174
324 394
325 181
326 340
327 203
328 353
329 561
330 527
331 582
332 556
333 63
334 295
335 285
336 232
337 124
338 286
339 562
340 205
341 182
342 643
343 585
344 299
345 354
346 211
347 401
348 185
349 396
350 344
351 586
352 645
353 593
354 535
355 240
356 206
357 95
358 327
359 564
360 800
361 402
362 356
363 307
364 301
365 417
366 213
367 186
368 539
369 404
370 227
371 594
372 568
373 771
374 418
375 649
376 302
377 832
378 551
379 111
380 896
381 360
382 588
383 609
384 331
385 214
386 309
387 188
388 449
389 217
390 646
391 408
392 229
393 541
394 159
395 420
396 596
397 650
398 773
399 310
400 333
401 119
402 657
403 658
404 610
405 368
406 339
407 391
408 313
409 218
410 334
411 542
412 230
413 233
414 774
415 612
416 175
417 123
418 652
419 600
420 450
421 583
422 341
423 220
424 555
425 314
426 557
427 424
428 395
429 777
430 673
431 355
432 287
433 183
434 234
435 125
436 616
437 342
438 563
439 778
440 660
441 558
442 452
443 674
444 397
445 785
446 432
447 316
448 345
449 241
450 207
451 403
452 357
453 187
454 587
455 565
456 664
457 624
458 780
459 236
460 126
461 242
462 398
463 705
464 346
465 456
466 358
467 405
468 303
469 569
470 189
471 595
472 215
473 566
474 676
475 361
476 706
477 589
478 244
479 786
480 647
481 348
482 419
483 406
484 464
485 801
486 590
487 362
488 570
489 409
490 680
491 597
492 788
493 572
494 219
495 311
496 708
497 598
498 601
499 651
500 421
501 792
502 802
503 611
504 602
505 369
506 190
507 688
508 653
509 248
510 231
511 410
512 364
513 654
514 659
515 335
516 480
517 315
518 221
519 613
520 422
521 370
522 425
523 235
524 451
525 543
526 614
527 412
528 343
529 222
530 775
531 317
532 372
533 426
534 453
535 237
536 559
537 833
538 804
539 712
540 834
541 661
542 808
543 779
544 617
545 604
546 433
547 720
548 816
549 836
550 347
551 897
552 243
553 662
554 454
555 318
556 675
557 618
558 898
559 781
560 376
561 428
562 665
563 736
564 567
565 840
566 625
567 238
568 359
569 457
570 399
571 787
572 677
573 434
574 349
575 458
576 678
577 245
578 666
579 363
580 591
581 127
582 620
583 407
584 782
585 436
586 465
587 626
588 571
589 246
590 681
591 350
592 707
593 460
594 599
595 668
596 789
597 249
598 411
599 682
600 573
601 365
602 803
603 790
604 709
605 440
606 466
607 793
608 574
609 371
610 423
611 689
612 603
613 366
614 628
615 250
616 413
617 468
618 655
619 481
620 900
621 805
622 191
623 373
624 615
625 684
626 427
627 710
628 794
629 605
630 414
631 252
632 713
633 374
634 848
635 690
636 632
637 806
638 482
639 429
640 904
641 809
642 455
643 223
644 663
645 835
646 692
647 619
648 472
649 714
650 796
651 721
652 837
653 716
654 864
655 810
656 606
657 912
658 722
659 696
660 377
661 817
662 435
663 484
664 621
665 812
666 319
667 430
668 838
669 667
670 239
671 378
672 459
673 437
674 622
675 627
676 488
677 380
678 818
679 461
680 496
681 669
682 679
683 724
684 841
685 629
686 351
687 467
688 438
689 737
690 247
691 462
692 441
693 442
694 469
695 251
696 683
697 842
698 738
699 899
700 670
701 783
702 849
703 820
704 728
705 928
706 791
707 367
708 901
709 630
710 685
711 844
712 633
713 711
714 253
715 691
716 824
717 902
718 686
719 740
720 850
721 375
722 444
723 470
724 483
725 905
726 415
727 485
728 795
729 473
730 634
731 744
732 852
733 960
734 865
735 693
736 797
737 906
738 715
739 807
740 474
741 636
742 694
743 254
744 717
745 575
746 811
747 697
748 866
749 798
750 379
751 431
752 913
753 607
754 489
755 723
756 486
757 908
758 718
759 813
760 476
761 856
762 839
763 725
764 698
765 914
766 752
767 868
768 819
769 814
770 439
771 929
772 490
773 623
774 671
775 739
776 916
777 463
778 843
779 381
780 497
781 930
782 821
783 726
784 961
785 872
786 492
787 631
788 729
789 700
790 443
791 741
792 845
793 920
794 382
795 822
796 851
797 730
798 498
799 880
800 742
801 445
802 471
803 635
804 932
805 687
806 903
807 825
808 500
809 846
810 745
811 826
812 732
813 446
814 962
815 936
816 475
817 853
818 867
819 637
820 907
821 487
822 695
823 746
824 828
825 753
826 854
827 857
828 504
829 799
830 909
831 719
832 638
833 915
834 477
835 255
836 964
837 699
838 748
839 869
840 944
841 491
842 754
843 910
844 858
845 917
846 478
847 968
848 870
849 815
850 383
851 727
852 493
853 873
854 701
855 931
856 756
857 860
858 499
859 731
860 823
861 702
862 918
863 921
864 874
865 494
866 976
867 760
868 933
869 881
870 501
871 743
872 922
873 876
874 847
875 934
876 827
877 733
878 882
879 502
880 447
881 992
882 937
883 963
884 747
885 505
886 855
887 924
888 734
889 829
890 938
891 884
892 506
893 965
894 749
895 945
896 966
897 755
898 859
899 940
900 830
901 911
902 871
903 888
904 479
905 946
906 750
907 969
908 861
909 757
910 970
911 919
912 875
913 758
914 508
915 862
916 639
917 948
918 977
919 923
920 972
921 761
922 877
923 952
924 495
925 703
926 935
927 978
928 883
929 762
930 503
931 925
932 878
933 735
934 993
935 885
936 939
937 994
938 980
939 926
940 764
941 941
942 967
943 886
944 831
945 947
946 507
947 889
948 984
949 751
950 942
951 996
952 971
953 890
954 509
955 949
956 973
957 1000
958 892
959 950
960 863
961 759
962 1008
963 510
964 979
965 953
966 763
967 974
968 954
969 879
970 981
971 982
972 927
973 995
974 765
975 956
976 887
977 985
978 997
979 986
980 943
981 891
982 998
983 766
984 511
985 988
986 1001
987 951
988 1002
989 893
990 975
991 894
992 1009
993 955
994 1004
995 1010
996 957
997 983
998 958
999 987
1000 1012
1001 999
1002 1016
1003 767
1004 989
1005 1003
1006 990
1007 1005
1008 895
1009 1011
1010 1013
1011 959
1012 1006
1013 1014
1014 1017
1015 1018
1016 991
1017 1020
1018 1007
1019 1015
1020 1019
1021 1021
1022 1022
1023 1023
Sequence Q17, having a sequence length of 512:
[0, 1, 2, 4, 8, 16, 32, 3, 5, 64, 9, 6, 17, 10, 18, 128, 12, 33, 65, 20, 256, 34, 24, 36, 7, 129, 66, 11, 40, 68, 130, 19, 13, 48, 14, 72, 257, 21, 132, 35, 258, 22, 80, 136, 25, 37, 260, 264, 26, 96, 38, 67, 41, 144, 28, 69, 42, 272, 49, 70, 160, 44, 131, 73, 288, 192, 50, 74, 52, 15, 133, 320, 81, 23, 134, 384, 76, 56, 259, 82, 137, 27, 97, 39, 84, 138, 145, 261, 29, 43, 98, 88, 140, 30, 146, 71, 262, 265, 161, 45, 100, 51, 148, 46, 75, 266, 273, 104, 162, 53, 193, 152, 77, 164, 268, 274, 54, 83, 57, 112, 135, 78, 289, 194, 85, 276, 58, 168, 139, 99, 86, 60, 280, 89, 290, 196, 141, 101, 147, 176, 142, 321, 90, 200, 31, 292, 322, 263, 149, 102, 105, 296, 304, 163, 92, 47, 267, 150, 208, 385, 386, 324, 106, 153, 165, 55, 328, 113, 154, 79, 269, 108, 224, 166, 195, 270, 275, 291, 169, 59, 114, 277, 156, 87, 197, 116, 170, 61, 281, 278, 177, 293, 388, 91, 198, 172, 120, 201, 336, 62, 282, 143, 103, 178, 294, 93, 202, 323, 392, 297, 107, 180, 151, 209, 284, 94, 204, 298, 400, 352, 325, 155, 210, 305, 300, 109, 184, 115, 167, 225, 326, 306, 157, 329, 110, 117, 212, 171, 330, 226, 387, 308, 216, 416, 271, 279, 158, 337, 118, 332, 389, 173, 121, 199, 179, 228, 338, 390, 122, 448, 312, 393, 283, 174, 394, 181, 340, 203, 353, 63, 295, 285, 232, 124, 286, 205, 182, 299, 354, 211, 401, 185, 396, 344, 240, 206, 95, 327, 402, 356, 307, 301, 417, 213, 186, 404, 227, 418, 302, 111, 360, 331, 214, 309, 188, 449, 217, 408, 229, 159, 420, 310, 333, 119, 368, 339, 391, 313, 218, 334, 230, 233, 175, 123, 450, 341, 220, 314, 424, 395, 355, 287, 183, 234, 125, 342, 452, 397, 432, 316, 345, 241, 207, 403, 357, 187, 236, 126, 242, 398, 346, 456, 358, 405, 303, 189, 215, 361, 244, 348, 419, 406, 464, 362, 409, 219, 311, 421, 369, 190, 248, 231, 410, 364, 335, 480, 315, 221, 422, 370, 425, 235, 451, 412, 343, 222, 317, 372, 426, 453, 237, 433, 347, 243, 454, 318, 376, 428, 238, 359, 457, 399, 434, 349, 458, 245, 363, 127, 407, 436, 465, 246, 350, 460, 249, 411, 365, 440, 466, 371, 423, 366, 250, 413, 468, 481, 191, 373, 427, 414, 252, 374, 482, 429, 455, 223, 472, 377, 435, 484, 319, 430, 239, 378, 459, 437, 488, 380, 461, 496, 351, 467, 438, 247, 462, 441, 442, 469, 251, 367, 253, 375, 444, 470, 483, 415, 485, 473, 474, 254, 379, 431, 489, 486, 476, 439, 490, 463, 381, 497, 492, 443, 382, 498, 445, 471, 500, 446, 475, 487, 504, 477, 255, 491, 478, 383, 493, 499, 494, 501, 502, 447, 505, 506, 479, 508, 495, 503, 507, 509, 510, 511]
TABLE Q17
having a sequence length of 512:
Reliability or sequence Polarized channel
number of reliability sequence number
0 0
1 1
2 2
3 4
4 8
5 16
6 32
7 3
8 5
9 64
10 9
11 6
12 17
13 10
14 18
15 128
16 12
17 33
18 65
19 20
20 256
21 34
22 24
23 36
24 7
25 129
26 66
27 11
28 40
29 68
30 130
31 19
32 13
33 48
34 14
35 72
36 257
37 21
38 132
39 35
40 258
41 22
42 80
43 136
44 25
45 37
46 260
47 264
48 26
49 96
50 38
51 67
52 41
53 144
54 28
55 69
56 42
57 272
58 49
59 70
60 160
61 44
62 131
63 73
64 288
65 192
66 50
67 74
68 52
69 15
70 133
71 320
72 81
73 23
74 134
75 384
76 76
77 56
78 259
79 82
80 137
81 27
82 97
83 39
84 84
85 138
86 145
87 261
88 29
89 43
90 98
91 88
92 140
93 30
94 146
95 71
96 262
97 265
98 161
99 45
100 100
101 51
102 148
103 46
104 75
105 266
106 273
107 104
108 162
109 53
110 193
111 152
112 77
113 164
114 268
115 274
116 54
117 83
118 57
119 112
120 135
121 78
122 289
123 194
124 85
125 276
126 58
127 168
128 139
129 99
130 86
131 60
132 280
133 89
134 290
135 196
136 141
137 101
138 147
139 176
140 142
141 321
142 90
143 200
144 31
145 292
146 322
147 263
148 149
149 102
150 105
151 296
152 304
153 163
154 92
155 47
156 267
157 150
158 208
159 385
160 386
161 324
162 106
163 153
164 165
165 55
166 328
167 113
168 154
169 79
170 269
171 108
172 224
173 166
174 195
175 270
176 275
177 291
178 169
179 59
180 114
181 277
182 156
183 87
184 197
185 116
186 170
187 61
188 281
189 278
190 177
191 293
192 388
193 91
194 198
195 172
196 120
197 201
198 336
199 62
200 282
201 143
202 103
203 178
204 294
205 93
206 202
207 323
208 392
209 297
210 107
211 180
212 151
213 209
214 284
215 94
216 204
217 298
218 400
219 352
220 325
221 155
222 210
223 305
224 300
225 109
226 184
227 115
228 167
229 225
230 326
231 306
232 157
233 329
234 110
235 117
236 212
237 171
238 330
239 226
240 387
241 308
242 216
243 416
244 271
245 279
246 158
247 337
248 118
249 332
250 389
251 173
252 121
253 199
254 179
255 228
256 338
257 390
258 122
259 448
260 312
261 393
262 283
263 174
264 394
265 181
266 340
267 203
268 353
269 63
270 295
271 285
272 232
273 124
274 286
275 205
276 182
277 299
278 354
279 211
280 401
281 185
282 396
283 344
284 240
285 206
286 95
287 327
288 402
289 356
290 307
291 301
292 417
293 213
294 186
295 404
296 227
297 418
298 302
299 111
300 360
301 331
302 214
303 309
304 188
305 449
306 217
307 408
308 229
309 159
310 420
311 310
312 333
313 119
314 368
315 339
316 391
317 313
318 218
319 334
320 230
321 233
322 175
323 123
324 450
325 341
326 220
327 314
328 424
329 395
330 355
331 287
332 183
333 234
334 125
335 342
336 452
337 397
338 432
339 316
340 345
341 241
342 207
343 403
344 357
345 187
346 236
347 126
348 242
349 398
350 346
351 456
352 358
353 405
354 303
355 189
356 215
357 361
358 244
359 348
360 419
361 406
362 464
363 362
364 409
365 219
366 311
367 421
368 369
369 190
370 248
371 231
372 410
373 364
374 335
375 480
376 315
377 221
378 422
379 370
380 425
381 235
382 451
383 412
384 343
385 222
386 317
387 372
388 426
389 453
390 237
391 433
392 347
393 243
394 454
395 318
396 376
397 428
398 238
399 359
400 457
401 399
402 434
403 349
404 458
405 245
406 363
407 127
408 407
409 436
410 465
411 246
412 350
413 460
414 249
415 411
416 365
417 440
418 466
419 371
420 423
421 366
422 250
423 413
424 468
425 481
426 191
427 373
428 427
429 414
430 252
431 374
432 482
433 429
434 455
435 223
436 472
437 377
438 435
439 484
440 319
441 430
442 239
443 378
444 459
445 437
446 488
447 380
448 461
449 496
450 351
451 467
452 438
453 247
454 462
455 441
456 442
457 469
458 251
459 367
460 253
461 375
462 444
463 470
464 483
465 415
466 485
467 473
468 474
469 254
470 379
471 431
472 489
473 486
474 476
475 439
476 490
477 463
478 381
479 497
480 492
481 443
482 382
483 498
484 445
485 471
486 500
487 446
488 475
489 487
490 504
491 477
492 255
493 491
494 478
495 383
496 493
497 499
498 494
499 501
500 502
501 447
502 505
503 506
504 479
505 508
506 495
507 503
508 507
509 509
510 510
511 511
Sequence Q18, having a sequence length of 256:
[0, 1, 2, 4, 8, 16, 32, 3, 5, 64, 9, 6, 17, 10, 18, 128, 12, 33, 65, 20, 34, 24, 36, 7, 129, 66, 11, 40, 68, 130, 19, 13, 48, 14, 72, 21, 132, 35, 22, 80, 136, 25, 37, 26, 96, 38, 67, 41, 144, 28, 69, 42, 49, 70, 160, 44, 131, 73, 192, 50, 74, 52, 15, 133, 81, 23, 134, 76, 56, 82, 137, 27, 97, 39, 84, 138, 145, 29, 43, 98, 88, 140, 30, 146, 71, 161, 45, 100, 51, 148, 46, 75, 104, 162, 53, 193, 152, 77, 164, 54, 83, 57, 112, 135, 78, 194, 85, 58, 168, 139, 99, 86, 60, 89, 196, 141, 101, 147, 176, 142, 90, 200, 31, 149, 102, 105, 163, 92, 47, 150, 208, 106, 153, 165, 55, 113, 154, 79, 108, 224, 166, 195, 169, 59, 114, 156, 87, 197, 116, 170, 61, 177, 91, 198, 172, 120, 201, 62, 143, 103, 178, 93, 202, 107, 180, 151, 209, 94, 204, 155, 210, 109, 184, 115, 167, 225, 157, 110, 117, 212, 171, 226, 216, 158, 118, 173, 121, 199, 179, 228, 122, 174, 181, 203, 63, 232, 124, 205, 182, 211, 185, 240, 206, 95, 213, 186, 227, 111, 214, 188, 217, 229, 159, 119, 218, 230, 233, 175, 123, 220, 183, 234, 125, 241, 207, 187, 236, 126, 242, 189, 215, 244, 219, 190, 248, 231, 221, 235, 222, 237, 243, 238, 245, 127, 246, 249, 250, 191, 252, 223, 239, 247, 251, 253, 254, 255]
TABLE Q18
having a sequence length of 256:
Reliability Polarized
or sequence channel
number of sequence
reliability number
0 0
1 1
2 2
3 4
4 8
5 16
6 32
7 3
8 5
9 64
10 9
11 6
12 17
13 10
14 18
15 128
16 12
17 33
18 65
19 20
20 34
21 24
22 36
23 7
24 129
25 66
26 11
27 40
28 68
29 130
30 19
31 13
32 48
33 14
34 72
35 21
36 132
37 35
38 22
39 80
40 136
41 25
42 37
43 26
44 96
45 38
46 67
47 41
48 144
49 28
50 69
51 42
52 49
53 70
54 160
55 44
56 131
57 73
58 192
59 50
60 74
61 52
62 15
63 133
64 81
65 23
66 134
67 76
68 56
69 82
70 137
71 27
72 97
73 39
74 84
75 138
76 145
77 29
78 43
79 98
80 88
81 140
82 30
83 146
84 71
85 161
86 45
87 100
88 51
89 148
90 46
91 75
92 104
93 162
94 53
95 193
96 152
97 77
98 164
99 54
100 83
101 57
102 112
103 135
104 78
105 194
106 85
107 58
108 168
109 139
110 99
111 86
112 60
113 89
114 196
115 141
116 101
117 147
118 176
119 142
120 90
121 200
122 31
123 149
124 102
125 105
126 163
127 92
128 47
129 150
130 208
131 106
132 153
133 165
134 55
135 113
136 154
137 79
138 108
139 224
140 166
141 195
142 169
143 59
144 114
145 156
146 87
147 197
148 116
149 170
150 61
151 177
152 91
153 198
154 172
155 120
156 201
157 62
158 143
159 103
160 178
161 93
162 202
163 107
164 180
165 151
166 209
167 94
168 204
169 155
170 210
171 109
172 184
173 115
174 167
175 225
176 157
177 110
178 117
179 212
180 171
181 226
182 216
183 158
184 118
185 173
186 121
187 199
188 179
189 228
190 122
191 174
192 181
193 203
194 63
195 232
196 124
197 205
198 182
199 211
200 185
201 240
202 206
203 95
204 213
205 186
206 227
207 111
208 214
209 188
210 217
211 229
212 159
213 119
214 218
215 230
216 233
217 175
218 123
219 220
220 183
221 234
222 125
223 241
224 207
225 187
226 236
227 126
228 242
229 189
230 215
231 244
232 219
233 190
234 248
235 231
236 221
237 235
238 222
239 237
240 243
241 238
242 245
243 127
244 246
245 249
246 250
247 191
248 252
249 223
250 239
251 247
252 251
253 253
254 254
255 255
Sequence Q19, having a sequence length of 128:
[0, 1, 2, 4, 8, 16, 32, 3, 5, 64, 9, 6, 17, 10, 18, 12, 33, 65, 20, 34, 24, 36, 7, 66, 11, 40, 68, 19, 13, 48, 14, 72, 21, 35, 22, 80, 25, 37, 26, 96, 38, 67, 41, 28, 69, 42, 49, 70, 44, 73, 50, 74, 52, 15, 81, 23, 76, 56, 82, 27, 97, 39, 84, 29, 43, 98, 88, 30, 71, 45, 100, 51, 46, 75, 104, 53, 77, 54, 83, 57, 112, 78, 85, 58, 99, 86, 60, 89, 101, 90, 31, 102, 105, 92, 47, 106, 55, 113, 79, 108, 59, 114, 87, 116, 61, 91, 120, 62, 103, 93, 107, 94, 109, 115, 110, 117, 118, 121, 122, 63, 124, 95, 111, 119, 123, 125, 126, 127]
TABLE Q19
having a sequence length of 128:
Reliability Polarized
or sequence channel
number of sequence
reliability number
0 0
1 1
2 2
3 4
4 8
5 16
6 32
7 3
8 5
9 64
10 9
11 6
12 17
13 10
14 18
15 12
16 33
17 65
18 20
19 34
20 24
21 36
22 7
23 66
24 11
25 40
26 68
27 19
28 13
29 48
30 14
31 72
32 21
33 35
34 22
35 80
36 25
37 37
38 26
39 96
40 38
41 67
42 41
43 28
44 69
45 42
46 49
47 70
48 44
49 73
50 50
51 74
52 52
53 15
54 81
55 23
56 76
57 56
58 82
59 27
60 97
61 39
62 84
63 29
64 43
65 98
66 88
67 30
68 71
69 45
70 100
71 51
72 46
73 75
74 104
75 53
76 77
77 54
78 83
79 57
80 112
81 78
82 85
83 58
84 99
85 86
86 60
87 89
88 101
89 90
90 31
91 102
92 105
93 92
94 47
95 106
96 55
97 113
98 79
99 108
100 59
101 114
102 87
103 116
104 61
105 91
106 120
107 62
108 103
109 93
110 107
111 94
112 109
113 115
114 110
115 117
116 118
117 121
118 122
119 63
120 124
121 95
122 111
123 119
124 123
125 125
126 126
127 127
Sequence Q20, having a sequence length of 64:
[0, 1, 2, 4, 8, 16, 32, 3, 5, 9, 6, 17, 10, 18, 12, 33, 20, 34, 24, 36, 7, 11, 40, 19, 13, 48, 14, 21, 35, 22, 25, 37, 26, 38, 41, 28, 42, 49, 44, 50, 52, 15, 23, 56, 27, 39, 29, 43, 30, 45, 51, 46, 53, 54, 57, 58, 60, 31, 47, 55, 59, 61, 62, 63]
TABLE Q20
having a sequence length of 64:
Reliability Polarized
or sequence channel
number of sequence
reliability number
0 0
1 1
2 2
3 4
4 8
5 16
6 32
7 3
8 5
9 9
10 6
11 17
12 10
13 18
14 12
15 33
16 20
17 34
18 24
19 36
20 7
21 11
22 40
23 19
24 13
25 48
26 14
27 21
28 35
29 22
30 25
31 37
32 26
33 38
34 41
35 28
36 42
37 49
38 44
39 50
40 52
41 15
42 23
43 56
44 27
45 39
46 29
47 43
48 30
49 45
50 51
51 46
52 53
53 54
54 57
55 58
56 60
57 31
58 47
59 55
60 59
61 61
62 62
63 63
Sequence Z16, having a sequence length of 1024:
[0, 1, 2, 7, 3, 8, 11, 24, 4, 10, 13, 28, 16, 33, 35, 76, 5, 12, 14, 32, 19, 38, 42, 80, 22, 46, 50, 88, 57, 95, 101, 162, 6, 17, 21, 40, 23, 47, 53, 90, 29, 55, 60, 96, 66, 108, 113, 175, 34, 62, 72, 111, 75, 120, 129, 186, 84, 131, 141, 209, 146, 218, 236, 333, 9, 18, 26, 54, 30, 58, 63, 103, 36, 68, 73, 114, 83, 123, 135, 193, 43, 79, 86, 130, 91, 138, 145, 214, 99, 148, 160, 228, 174, 242, 256, 357, 51, 89, 97, 144, 109, 154, 169, 239, 118, 170, 183, 250, 195, 269, 282, 379, 133, 191, 211, 271, 216, 283, 301, 401, 233, 307, 315, 417, 337, 435, 460, 581, 15, 25, 31, 67, 39, 77, 81, 134, 44, 87, 92, 143, 100, 153, 157, 238, 56, 93, 102, 155, 112, 168, 177, 252, 122, 184, 192, 264, 213, 279, 297, 394, 65, 106, 119, 173, 124, 185, 198, 273, 142, 208, 217, 285, 232, 306, 323, 416, 156, 225, 240, 311, 251, 325, 341, 433, 270, 348, 367, 453, 387, 470, 506, 622, 71, 121, 137, 201, 152, 215, 231, 309, 161, 234, 244, 327, 257, 340, 356, 450, 178, 253, 265, 346, 284, 366, 385, 472, 293, 389, 409, 494, 423, 518, 529, 643, 197, 274, 287, 370, 312, 392, 412, 510, 336, 413, 434, 523, 459, 535, 567, 670, 355, 449, 461, 552, 478, 577, 589, 690, 509, 597, 615, 695, 631, 714, 743, 835, 20, 37, 41, 85, 48, 94, 104, 167, 49, 105, 115, 176, 126, 194, 202, 295, 61, 116, 127, 205, 139, 212, 223, 296, 147, 222, 237, 321, 254, 335, 338, 432, 69, 136, 149, 207, 164, 226, 241, 334, 171, 248, 258, 344, 268, 364, 376, 468, 172, 266, 277, 363, 292, 386, 399, 495, 318, 408, 425, 517, 447, 531, 555, 666, 78, 159, 165, 246, 182, 262, 276, 358, 187, 281, 286, 384, 302, 400, 410, 515, 235, 298, 313, 406, 326, 422, 437, 528, 350, 448, 464, 550, 481, 574, 591, 686, 260, 328, 345, 431, 362, 452, 466, 568, 381, 475, 487, 579, 512, 601, 613, 707, 405, 505, 521, 609, 532, 623, 633, 721, 560, 660, 671, 750, 677, 779, 794, 850, 82, 179, 181, 291, 227, 305, 314, 407, 247, 320, 324, 428, 349, 444, 462, 570, 259, 347, 361, 451, 369, 467, 483, 583, 391, 489, 511, 598, 527, 616, 630, 726, 294, 365, 374, 482, 395, 500, 520, 610, 427, 522, 533, 626, 561, 639, 667, 751, 446, 546, 573, 662, 585, 673, 688, 770, 605, 692, 693, 790, 722, 801, 813, 880, 317, 388, 420, 524, 442, 534, 554, 642, 465, 569, 575, 672, 593, 679, 691, 777, 484, 586, 606, 687, 617, 694, 723, 802, 648, 729, 740, 816, 760, 834, 846, 904, 516, 619, 638, 724, 663, 727, 756, 821, 676, 754, 772, 841, 786, 852, 865, 924, 680, 780, 798, 858, 808, 870, 879, 930, 828, 885, 892, 946, 914, 954, 963, 984, 27, 45, 52, 98, 59, 117, 128, 199, 64, 132, 140, 204, 151, 220, 224, 330, 70, 150, 158, 219, 166, 263, 272, 354, 188, 275, 290, 368, 304, 393, 411, 525, 74, 163, 180, 267, 190, 288, 299, 378, 200, 308, 316, 424, 332, 426, 441, 536, 210, 329, 339, 438, 359, 455, 473, 564, 372, 469, 488, 588, 493, 600, 608, 745, 107, 189, 196, 303, 206, 319, 331, 421, 229, 343, 351, 454, 382, 477, 486, 580, 245, 353, 371, 471, 396, 491, 497, 594, 419, 498, 504, 612, 545, 629, 656, 753, 261, 383, 404, 503, 415, 519, 526, 624, 436, 544, 557, 647, 582, 664, 674, 773, 457, 566, 587, 675, 614, 685, 709, 787, 636, 712, 730, 803, 741, 819, 832, 916, 110, 203, 221, 342, 243, 352, 390, 480, 255, 375, 397, 499, 418, 508, 513, 618, 280, 402, 403, 514, 440, 541, 553, 644, 456, 562, 578, 669, 595, 681, 700, 774, 300, 430, 443, 556, 474, 572, 576, 682, 490, 590, 599, 696, 625, 710, 718, 805, 507, 611, 635, 715, 646, 735, 742, 822, 659, 747, 764, 837, 789, 854, 861, 925, 322, 463, 476, 592, 496, 604, 627, 713, 539, 632, 649, 738, 653, 744, 758, 831, 547, 651, 658, 755, 683, 763, 783, 851, 704, 788, 797, 859, 812, 877, 888, 933, 563, 689, 698, 775, 719, 791, 800, 871, 731, 810, 823, 884, 838, 894, 906, 949, 766, 825, 842, 897, 856, 909, 913, 961, 867, 921, 929, 966, 940, 974, 983, 1003, 125, 230, 249, 373, 278, 398, 414, 530, 289, 429, 439, 543, 458, 559, 584, 701, 310, 445, 479, 571, 492, 596, 603, 706, 501, 607, 628, 728, 650, 736, 749, 829, 360, 485, 502, 602, 538, 621, 637, 739, 542, 641, 655, 746, 665, 759, 769, 849, 548, 661, 678, 768, 703, 782, 795, 860, 716, 807, 811, 876, 824, 889, 900, 944, 377, 537, 540, 645, 549, 652, 668, 762, 565, 684, 697, 778, 711, 792, 809, 874, 634, 702, 720, 796, 732, 817, 826, 886, 761, 827, 844, 898, 857, 908, 915, 960, 654, 734, 748, 818, 767, 839, 848, 902, 785, 853, 864, 912, 873, 922, 932, 969, 799, 869, 878, 928, 891, 935, 943, 976, 903, 947, 953, 981, 958, 989, 991, 1008, 380, 551, 558, 699, 620, 708, 717, 806, 640, 725, 737, 820, 757, 830, 843, 901, 657, 752, 765, 833, 776, 845, 862, 911, 793, 863, 872, 919, 887, 931, 939, 972, 705, 771, 781, 855, 804, 868, 875, 926, 815, 882, 890, 936, 899, 941, 950, 980, 840, 895, 905, 945, 917, 955, 959, 987, 923, 965, 968, 993, 975, 996, 998, 1011, 733, 784, 814, 883, 836, 893, 896, 942, 847, 907, 910, 952, 920, 956, 967, 990, 866, 918, 927, 964, 938, 970, 971, 997, 948, 977, 979, 999, 985, 1004, 1006, 1016, 881, 934, 937, 973, 951, 978, 982, 1001, 957, 986, 988, 1005, 994, 1007, 1012, 1018, 962, 992, 995, 1009, 1000, 1010, 1013, 1019, 1002, 1014, 1015, 1020, 1017, 1021, 1022, 1023]
TABLE Z16
having a sequence length of 1024.
Polarized Reliability
channel or sequence
sequence number of
number reliability
0 0
1 1
2 2
3 7
4 3
5 8
6 11
7 24
8 4
9 10
10 13
11 28
12 16
13 33
14 35
15 76
16 5
17 12
18 14
19 32
20 19
21 38
22 42
23 80
24 22
25 46
26 50
27 88
28 57
29 95
30 101
31 162
32 6
33 17
34 21
35 40
36 23
37 47
38 53
39 90
40 29
41 55
42 60
43 96
44 66
45 108
46 113
47 175
48 34
49 62
50 72
51 111
52 75
53 120
54 129
55 186
56 84
57 131
58 141
59 209
60 146
61 218
62 236
63 333
64 9
65 18
66 26
67 54
68 30
69 58
70 63
71 103
72 36
73 68
74 73
75 114
76 83
77 123
78 135
79 193
80 43
81 79
82 86
83 130
84 91
85 138
86 145
87 214
88 99
89 148
90 160
91 228
92 174
93 242
94 256
95 357
96 51
97 89
98 97
99 144
100 109
101 154
102 169
103 239
104 118
105 170
106 183
107 250
108 195
109 269
110 282
111 379
112 133
113 191
114 211
115 271
116 216
117 283
118 301
119 401
120 233
121 307
122 315
123 417
124 337
125 435
126 460
127 581
128 15
129 25
130 31
131 67
132 39
133 77
134 81
135 134
136 44
137 87
138 92
139 143
140 100
141 153
142 157
143 238
144 56
145 93
146 102
147 155
148 112
149 168
150 177
151 252
152 122
153 184
154 192
155 264
156 213
157 279
158 297
159 394
160 65
161 106
162 119
163 173
164 124
165 185
166 198
167 273
168 142
169 208
170 217
171 285
172 232
173 306
174 323
175 416
176 156
177 225
178 240
179 311
180 251
181 325
182 341
183 433
184 270
185 348
186 367
187 453
188 387
189 470
190 506
191 622
192 71
193 121
194 137
195 201
196 152
197 215
198 231
199 309
200 161
201 234
202 244
203 327
204 257
205 340
206 356
207 450
208 178
209 253
210 265
211 346
212 284
213 366
214 385
215 472
216 293
217 389
218 409
219 494
220 423
221 518
222 529
223 643
224 197
225 274
226 287
227 370
228 312
229 392
230 412
231 510
232 336
233 413
234 434
235 523
236 459
237 535
238 567
239 670
240 355
241 449
242 461
243 552
244 478
245 577
246 589
247 690
248 509
249 597
250 615
251 695
252 631
253 714
254 743
255 835
256 20
257 37
258 41
259 85
260 48
261 94
262 104
263 167
264 49
265 105
266 115
267 176
268 126
269 194
270 202
271 295
272 61
273 116
274 127
275 205
276 139
277 212
278 223
279 296
280 147
281 222
282 237
283 321
284 254
285 335
286 338
287 432
288 69
289 136
290 149
291 207
292 164
293 226
294 241
295 334
296 171
297 248
298 258
299 344
300 268
301 364
302 376
303 468
304 172
305 266
306 277
307 363
308 292
309 386
310 399
311 495
312 318
313 408
314 425
315 517
316 447
317 531
318 555
319 666
320 78
321 159
322 165
323 246
324 182
325 262
326 276
327 358
328 187
329 281
330 286
331 384
332 302
333 400
334 410
335 515
336 235
337 298
338 313
339 406
340 326
341 422
342 437
343 528
344 350
345 448
346 464
347 550
348 481
349 574
350 591
351 686
352 260
353 328
354 345
355 431
356 362
357 452
358 466
359 568
360 381
361 475
362 487
363 579
364 512
365 601
366 613
367 707
368 405
369 505
370 521
371 609
372 532
373 623
374 633
375 721
376 560
377 660
378 671
379 750
380 677
381 779
382 794
383 850
384 82
385 179
386 181
387 291
388 227
389 305
390 314
391 407
392 247
393 320
394 324
395 428
396 349
397 444
398 462
399 570
400 259
401 347
402 361
403 451
404 369
405 467
406 483
407 583
408 391
409 489
410 511
411 598
412 527
413 616
414 630
415 726
416 294
417 365
418 374
419 482
420 395
421 500
422 520
423 610
424 427
425 522
426 533
427 626
428 561
429 639
430 667
431 751
432 446
433 546
434 573
435 662
436 585
437 673
438 688
439 770
440 605
441 692
442 693
443 790
444 722
445 801
446 813
447 880
448 317
449 388
450 420
451 524
452 442
453 534
454 554
455 642
456 465
457 569
458 575
459 672
460 593
461 679
462 691
463 777
464 484
465 586
466 606
467 687
468 617
469 694
470 723
471 802
472 648
473 729
474 740
475 816
476 760
477 834
478 846
479 904
480 516
481 619
482 638
483 724
484 663
485 727
486 756
487 821
488 676
489 754
490 772
491 841
492 786
493 852
494 865
495 924
496 680
497 780
498 798
499 858
500 808
501 870
502 879
503 930
504 828
505 885
506 892
507 946
508 914
509 954
510 963
511 984
512 27
513 45
514 52
515 98
516 59
517 117
518 128
519 199
520 64
521 132
522 140
523 204
524 151
525 220
526 224
527 330
528 70
529 150
530 158
531 219
532 166
533 263
534 272
535 354
536 188
537 275
538 290
539 368
540 304
541 393
542 411
543 525
544 74
545 163
546 180
547 267
548 190
549 288
550 299
551 378
552 200
553 308
554 316
555 424
556 332
557 426
558 441
559 536
560 210
561 329
562 339
563 438
564 359
565 455
566 473
567 564
568 372
569 469
570 488
571 588
572 493
573 600
574 608
575 745
576 107
577 189
578 196
579 303
580 206
581 319
582 331
583 421
584 229
585 343
586 351
587 454
588 382
589 477
590 486
591 580
592 245
593 353
594 371
595 471
596 396
597 491
598 497
599 594
600 419
601 498
602 504
603 612
604 545
605 629
606 656
607 753
608 261
609 383
610 404
611 503
612 415
613 519
614 526
615 624
616 436
617 544
618 557
619 647
620 582
621 664
622 674
623 773
624 457
625 566
626 587
627 675
628 614
629 685
630 709
631 787
632 636
633 712
634 730
635 803
636 741
637 819
638 832
639 916
640 110
641 203
642 221
643 342
644 243
645 352
646 390
647 480
648 255
649 375
650 397
651 499
652 418
653 508
654 513
655 618
656 280
657 402
658 403
659 514
660 440
661 541
662 553
663 644
664 456
665 562
666 578
667 669
668 595
669 681
670 700
671 774
672 300
673 430
674 443
675 556
676 474
677 572
678 576
679 682
680 490
681 590
682 599
683 696
684 625
685 710
686 718
687 805
688 507
689 611
690 635
691 715
692 646
693 735
694 742
695 822
696 659
697 747
698 764
699 837
700 789
701 854
702 861
703 925
704 322
705 463
706 476
707 592
708 496
709 604
710 627
711 713
712 539
713 632
714 649
715 738
716 653
717 744
718 758
719 831
720 547
721 651
722 658
723 755
724 683
725 763
726 783
727 851
728 704
729 788
730 797
731 859
732 812
733 877
734 888
735 933
736 563
737 689
738 698
739 775
740 719
741 791
742 800
743 871
744 731
745 810
746 823
747 884
748 838
749 894
750 906
751 949
752 766
753 825
754 842
755 897
756 856
757 909
758 913
759 961
760 867
761 921
762 929
763 966
764 940
765 974
766 983
767 1003
768 125
769 230
770 249
771 373
772 278
773 398
774 414
775 530
776 289
777 429
778 439
779 543
780 458
781 559
782 584
783 701
784 310
785 445
786 479
787 571
788 492
789 596
790 603
791 706
792 501
793 607
794 628
795 728
796 650
797 736
798 749
799 829
800 360
801 485
802 502
803 602
804 538
805 621
806 637
807 739
808 542
809 641
810 655
811 746
812 665
813 759
814 769
815 849
816 548
817 661
818 678
819 768
820 703
821 782
822 795
823 860
824 716
825 807
826 811
827 876
828 824
829 889
830 900
831 944
832 377
833 537
834 540
835 645
836 549
837 652
838 668
839 762
840 565
841 684
842 697
843 778
844 711
845 792
846 809
847 874
848 634
849 702
850 720
851 796
852 732
853 817
854 826
855 886
856 761
857 827
858 844
859 898
860 857
861 908
862 915
863 960
864 654
865 734
866 748
867 818
868 767
869 839
870 848
871 902
872 785
873 853
874 864
875 912
876 873
877 922
878 932
879 969
880 799
881 869
882 878
883 928
884 891
885 935
886 943
887 976
888 903
889 947
890 953
891 981
892 958
893 989
894 991
895 1008
896 380
897 551
898 558
899 699
900 620
901 708
902 717
903 806
904 640
905 725
906 737
907 820
908 757
909 830
910 843
911 901
912 657
913 752
914 765
915 833
916 776
917 845
918 862
919 911
920 793
921 863
922 872
923 919
924 887
925 931
926 939
927 972
928 705
929 771
930 781
931 855
932 804
933 868
934 875
935 926
936 815
937 882
938 890
939 936
940 899
941 941
942 950
943 980
944 840
945 895
946 905
947 945
948 917
949 955
950 959
951 987
952 923
953 965
954 968
955 993
956 975
957 996
958 998
959 1011
960 733
961 784
962 814
963 883
964 836
965 893
966 896
967 942
968 847
969 907
970 910
971 952
972 920
973 956
974 967
975 990
976 866
977 918
978 927
979 964
980 938
981 970
982 971
983 997
984 948
985 977
986 979
987 999
988 985
989 1004
990 1006
991 1016
992 881
993 934
994 937
995 973
996 951
997 978
998 982
999 1001
1000 957
1001 986
1002 988
1003 1005
1004 994
1005 1007
1006 1012
1007 1018
1008 962
1009 992
1010 995
1011 1009
1012 1000
1013 1010
1014 1013
1015 1019
1016 1002
1017 1014
1018 1015
1019 1020
1020 1017
1021 1021
1022 1022
1023 1023
Sequence Z17, having a sequence length of 512:
[0, 1, 2, 7, 3, 8, 11, 24, 4, 10, 13, 27, 16, 32, 34, 69, 5, 12, 14, 31, 19, 37, 41, 73, 22, 44, 48, 81, 54, 88, 93, 144, 6, 17, 21, 39, 23, 45, 50, 83, 28, 52, 56, 89, 61, 99, 103, 155, 33, 58, 66, 101, 68, 109, 116, 165, 77, 118, 126, 179, 131, 187, 199, 269, 9, 18, 26, 51, 29, 55, 59, 95, 35, 63, 67, 104, 76, 112, 121, 169, 42, 72, 79, 117, 84, 124, 130, 183, 91, 133, 142, 193, 154, 205, 215, 286, 49, 82, 90, 129, 100, 137, 149, 202, 107, 150, 162, 210, 171, 225, 234, 299, 119, 167, 180, 227, 185, 235, 248, 313, 196, 252, 258, 323, 273, 334, 347, 407, 15, 25, 30, 62, 38, 70, 74, 120, 43, 80, 85, 128, 92, 136, 140, 201, 53, 86, 94, 138, 102, 148, 157, 212, 111, 163, 168, 221, 182, 232, 246, 309, 60, 98, 108, 153, 113, 164, 173, 228, 127, 178, 186, 237, 195, 251, 263, 322, 139, 190, 203, 254, 211, 265, 276, 332, 226, 281, 294, 345, 304, 355, 369, 426, 65, 110, 123, 174, 135, 184, 194, 253, 143, 197, 206, 267, 216, 275, 285, 342, 158, 213, 222, 279, 236, 293, 302, 356, 242, 306, 318, 365, 326, 377, 385, 435, 172, 229, 239, 296, 255, 308, 320, 371, 272, 321, 333, 381, 346, 390, 398, 442, 284, 341, 348, 393, 358, 405, 411, 453, 370, 414, 422, 458, 430, 460, 469, 492, 20, 36, 40, 78, 46, 87, 96, 147, 47, 97, 105, 156, 114, 170, 175, 244, 57, 106, 115, 176, 125, 181, 189, 245, 132, 188, 200, 262, 214, 271, 274, 331, 64, 122, 134, 177, 145, 191, 204, 270, 151, 209, 217, 277, 224, 291, 298, 354, 152, 223, 231, 290, 241, 303, 311, 366, 260, 317, 327, 376, 339, 386, 395, 440, 71, 141, 146, 207, 161, 220, 230, 287, 166, 233, 238, 301, 249, 312, 319, 374, 198, 247, 256, 315, 266, 325, 335, 384, 283, 340, 350, 392, 359, 403, 412, 450, 219, 268, 278, 330, 289, 344, 352, 399, 300, 357, 363, 406, 373, 416, 421, 459, 314, 368, 379, 419, 387, 427, 431, 461, 396, 437, 443, 470, 447, 478, 482, 495, 75, 159, 160, 240, 192, 250, 257, 316, 208, 261, 264, 329, 282, 337, 349, 401, 218, 280, 288, 343, 295, 353, 361, 408, 307, 364, 372, 415, 383, 423, 429, 465, 243, 292, 297, 360, 310, 367, 378, 420, 328, 380, 388, 428, 397, 433, 441, 471, 338, 391, 402, 438, 409, 445, 452, 475, 417, 455, 456, 481, 462, 484, 487, 501, 259, 305, 324, 382, 336, 389, 394, 434, 351, 400, 404, 444, 413, 448, 454, 477, 362, 410, 418, 451, 424, 457, 463, 485, 436, 467, 468, 488, 474, 491, 494, 504, 375, 425, 432, 464, 439, 466, 473, 489, 446, 472, 476, 493, 480, 496, 498, 506, 449, 479, 483, 497, 486, 499, 500, 507, 490, 502, 503, 508, 505, 509, 510, 511]
TABLE Z17
having a sequence length of 512:
Polarized Reliability
channel or sequence
sequence number of
number reliability
0 0
1 1
2 2
3 7
4 3
5 8
6 11
7 24
8 4
9 10
10 13
11 27
12 16
13 32
14 34
15 69
16 5
17 12
18 14
19 31
20 19
21 37
22 41
23 73
24 22
25 44
26 48
27 81
28 54
29 88
30 93
31 144
32 6
33 17
34 21
35 39
36 23
37 45
38 50
39 83
40 28
41 52
42 56
43 89
44 61
45 99
46 103
47 155
48 33
49 58
50 66
51 101
52 68
53 109
54 116
55 165
56 77
57 118
58 126
59 179
60 131
61 187
62 199
63 269
64 9
65 18
66 26
67 51
68 29
69 55
70 59
71 95
72 35
73 63
74 67
75 104
76 76
77 112
78 121
79 169
80 42
81 72
82 79
83 117
84 84
85 124
86 130
87 183
88 91
89 133
90 142
91 193
92 154
93 205
94 215
95 286
96 49
97 82
98 90
99 129
100 100
101 137
102 149
103 202
104 107
105 150
106 162
107 210
108 171
109 225
110 234
111 299
112 119
113 167
114 180
115 227
116 185
117 235
118 248
119 313
120 196
121 252
122 258
123 323
124 273
125 334
126 347
127 407
128 15
129 25
130 30
131 62
132 38
133 70
134 74
135 120
136 43
137 80
138 85
139 128
140 92
141 136
142 140
143 201
144 53
145 86
146 94
147 138
148 102
149 148
150 157
151 212
152 111
153 163
154 168
155 221
156 182
157 232
158 246
159 309
160 60
161 98
162 108
163 153
164 113
165 164
166 173
167 228
168 127
169 178
170 186
171 237
172 195
173 251
174 263
175 322
176 139
177 190
178 203
179 254
180 211
181 265
182 276
183 332
184 226
185 281
186 294
187 345
188 304
189 355
190 369
191 426
192 65
193 110
194 123
195 174
196 135
197 184
198 194
199 253
200 143
201 197
202 206
203 267
204 216
205 275
206 285
207 342
208 158
209 213
210 222
211 279
212 236
213 293
214 302
215 356
216 242
217 306
218 318
219 365
220 326
221 377
222 385
223 435
224 172
225 229
226 239
227 296
228 255
229 308
230 320
231 371
232 272
233 321
234 333
235 381
236 346
237 390
238 398
239 442
240 284
241 341
242 348
243 393
244 358
245 405
246 411
247 453
248 370
249 414
250 422
251 458
252 430
253 460
254 469
255 492
256 20
257 36
258 40
259 78
260 46
261 87
262 96
263 147
264 47
265 97
266 105
267 156
268 114
269 170
270 175
271 244
272 57
273 106
274 115
275 176
276 125
277 181
278 189
279 245
280 132
281 188
282 200
283 262
284 214
285 271
286 274
287 331
288 64
289 122
290 134
291 177
292 145
293 191
294 204
295 270
296 151
297 209
298 217
299 277
300 224
301 291
302 298
303 354
304 152
305 223
306 231
307 290
308 241
309 303
310 311
311 366
312 260
313 317
314 327
315 376
316 339
317 386
318 395
319 440
320 71
321 141
322 146
323 207
324 161
325 220
326 230
327 287
328 166
329 233
330 238
331 301
332 249
333 312
334 319
335 374
336 198
337 247
338 256
339 315
340 266
341 325
342 335
343 384
344 283
345 340
346 350
347 392
348 359
349 403
350 412
351 450
352 219
353 268
354 278
355 330
356 289
357 344
358 352
359 399
360 300
361 357
362 363
363 406
364 373
365 416
366 421
367 459
368 314
369 368
370 379
371 419
372 387
373 427
374 431
375 461
376 396
377 437
378 443
379 470
380 447
381 478
382 482
383 495
384 75
385 159
386 160
387 240
388 192
389 250
390 257
391 316
392 208
393 261
394 264
395 329
396 282
397 337
398 349
399 401
400 218
401 280
402 288
403 343
404 295
405 353
406 361
407 408
408 307
409 364
410 372
411 415
412 383
413 423
414 429
415 465
416 243
417 292
418 297
419 360
420 310
421 367
422 378
423 420
424 328
425 380
426 388
427 428
428 397
429 433
430 441
431 471
432 338
433 391
434 402
435 438
436 409
437 445
438 452
439 475
440 417
441 455
442 456
443 481
444 462
445 484
446 487
447 501
448 259
449 305
450 324
451 382
452 336
453 389
454 394
455 434
456 351
457 400
458 404
459 444
460 413
461 448
462 454
463 477
464 362
465 410
466 418
467 451
468 424
469 457
470 463
471 485
472 436
473 467
474 468
475 488
476 474
477 491
478 494
479 504
480 375
481 425
482 432
483 464
484 439
485 466
486 473
487 489
488 446
489 472
490 476
491 493
492 480
493 496
494 498
495 506
496 449
497 479
498 483
499 497
500 486
501 499
502 500
503 507
504 490
505 502
506 503
507 508
508 505
509 509
510 510
511 511
Sequence Z18, having a sequence length of 256:
[0, 1, 2, 7, 3, 8, 11, 23, 4, 10, 13, 26, 16, 31, 33, 62, 5, 12, 14, 30, 19, 35, 38, 65, 21, 41, 43, 71, 49, 77, 82, 122, 6, 17, 20, 37, 22, 42, 45, 73, 27, 47, 51, 78, 55, 86, 90, 128, 32, 52, 59, 88, 61, 94, 99, 134, 68, 101, 107, 143, 112, 150, 157, 194, 9, 18, 25, 46, 28, 50, 53, 84, 34, 57, 60, 91, 67, 97, 104, 137, 39, 64, 69, 100, 74, 106, 111, 146, 80, 113, 120, 152, 127, 161, 167, 203, 44, 72, 79, 110, 87, 116, 124, 159, 92, 125, 131, 163, 138, 171, 177, 207, 102, 135, 144, 173, 148, 178, 184, 213, 155, 186, 190, 218, 196, 222, 227, 243, 15, 24, 29, 56, 36, 63, 66, 103, 40, 70, 75, 109, 81, 115, 119, 158, 48, 76, 83, 117, 89, 123, 129, 165, 96, 132, 136, 169, 145, 176, 183, 212, 54, 85, 93, 126, 98, 133, 140, 174, 108, 142, 149, 180, 154, 185, 191, 217, 118, 151, 160, 188, 164, 192, 198, 220, 172, 200, 205, 225, 209, 229, 233, 247, 58, 95, 105, 141, 114, 147, 153, 187, 121, 156, 162, 193, 168, 197, 202, 224, 130, 166, 170, 199, 179, 204, 208, 230, 182, 210, 214, 232, 219, 236, 238, 249, 139, 175, 181, 206, 189, 211, 215, 235, 195, 216, 221, 237, 226, 239, 241, 250, 201, 223, 228, 240, 231, 242, 244, 251, 234, 245, 246, 252, 248, 253, 254, 255]
TABLE Z18
having a sequence length of 256:
Polarized Reliability
channel or sequence
sequence number of
number reliability
0 0
1 1
2 2
3 7
4 3
5 8
6 11
7 23
8 4
9 10
10 13
11 26
12 16
13 31
14 33
15 62
16 5
17 12
18 14
19 30
20 19
21 35
22 38
23 65
24 21
25 41
26 43
27 71
28 49
29 77
30 82
31 122
32 6
33 17
34 20
35 37
36 22
37 42
38 45
39 73
40 27
41 47
42 51
43 78
44 55
45 86
46 90
47 128
48 32
49 52
50 59
51 88
52 61
53 94
54 99
55 134
56 68
57 101
58 107
59 143
60 112
61 150
62 157
63 194
64 9
65 18
66 25
67 46
68 28
69 50
70 53
71 84
72 34
73 57
74 60
75 91
76 67
77 97
78 104
79 137
80 39
81 64
82 69
83 100
84 74
85 106
86 111
87 146
88 80
89 113
90 120
91 152
92 127
93 161
94 167
95 203
96 44
97 72
98 79
99 110
100 87
101 116
102 124
103 159
104 92
105 125
106 131
107 163
108 138
109 171
110 177
111 207
112 102
113 135
114 144
115 173
116 148
117 178
118 184
119 213
120 155
121 186
122 190
123 218
124 196
125 222
126 227
127 243
128 15
129 24
130 29
131 56
132 36
133 63
134 66
135 103
136 40
137 70
138 75
139 109
140 81
141 115
142 119
143 158
144 48
145 76
146 83
147 117
148 89
149 123
150 129
151 165
152 96
153 132
154 136
155 169
156 145
157 176
158 183
159 212
160 54
161 85
162 93
163 126
164 98
165 133
166 140
167 174
168 108
169 142
170 149
171 180
172 154
173 185
174 191
175 217
176 118
177 151
178 160
179 188
180 164
181 192
182 198
183 220
184 172
185 200
186 205
187 225
188 209
189 229
190 233
191 247
192 58
193 95
194 105
196 114
197 147
198 153
199 187
200 121
201 156
202 162
203 193
204 168
205 197
206 202
207 224
208 130
209 166
210 170
211 199
212 179
213 204
214 208
215 230
216 182
217 210
218 214
219 232
220 219
221 236
222 238
223 249
224 139
225 175
226 181
227 206
228 189
229 211
230 215
231 235
232 195
233 216
234 221
235 237
236 226
237 239
238 241
239 250
240 201
241 223
242 228
243 240
244 231
245 242
246 244
247 251
248 234
249 245
250 246
251 252
252 248
253 253
254 254
255 255
Sequence Z19, having a sequence length of 128:
[0, 1, 2, 7, 3, 8, 11, 22, 4, 10, 13, 24, 15, 28, 30, 53, 5, 12, 14, 27, 18, 32, 34, 55, 20, 36, 38, 59, 43, 63, 67, 90, 6, 16, 19, 33, 21, 37, 40, 61, 25, 42, 45, 64, 48, 69, 72, 94, 29, 46, 50, 71, 52, 75, 77, 96, 57, 79, 83, 100, 86, 104, 107, 119, 9, 17, 23, 41, 26, 44, 47, 68, 31, 49, 51, 73, 56, 76, 81, 98, 35, 54, 58, 78, 62, 82, 85, 102, 66, 87, 89, 105, 93, 109, 111, 121, 39, 60, 65, 84, 70, 88, 91, 108, 74, 92, 95, 110, 99, 112, 114, 122, 80, 97, 101, 113, 103, 115, 116, 123, 106, 117, 118, 124, 120, 125, 126, 127]
TABLE Z19
having a sequence length of 128:
Polarized Reliability
channel or sequence
sequence number of
number reliability
0 0
1 1
2 2
3 7
4 3
5 8
6 11
7 22
8 4
9 10
10 13
11 24
12 15
13 28
14 30
15 53
16 5
17 12
18 14
19 27
20 18
21 32
22 34
23 55
24 20
25 36
26 38
27 59
28 43
29 63
30 67
31 90
32 6
33 16
34 19
35 33
36 21
37 37
38 40
39 61
40 25
41 42
42 45
43 64
44 48
45 69
46 72
47 94
48 29
49 46
50 50
51 71
52 52
53 75
54 77
55 96
57 79
58 83
59 100
60 86
61 104
62 107
63 119
64 9
65 17
66 23
67 41
68 26
69 44
70 47
71 68
72 31
73 49
74 51
75 73
76 56
77 76
78 81
79 98
80 35
81 54
82 58
83 78
84 62
85 82
86 85
87 102
88 66
89 87
90 89
91 105
92 93
93 109
94 111
95 121
96 39
97 60
98 65
99 84
100 70
101 88
102 91
103 108
104 74
105 92
106 95
107 110
108 99
109 112
110 114
111 122
112 80
113 97
114 101
115 113
116 103
117 115
118 116
119 123
120 106
121 117
122 118
123 124
124 120
125 125
126 126
127 127
Sequence Z20, having a sequence length of 64:
[0, 1, 2, 7, 3, 8, 10, 20, 4, 9, 12, 21, 14, 24, 26, 41, 5, 11, 13, 23, 16, 27, 29, 42, 18, 30, 32, 44, 35, 46, 48, 57, 6, 15, 17, 28, 19, 31, 33, 45, 22, 34, 36, 47, 38, 49, 51, 58, 25, 37, 39, 50, 40, 52, 53, 59, 43, 54, 55, 60, 56, 61, 62, 63]
TABLE Z20
having a sequence length of 64:
Polarized Reliability
channel or sequence
sequence number of
number reliability
0 0
1 1
2 2
3 7
4 3
5 8
6 10
7 20
8 4
9 9
10 12
11 21
12 14
13 24
14 26
15 41
16 5
17 11
18 13
19 23
20 16
21 27
22 29
23 42
24 18
25 30
26 32
27 44
28 35
29 46
30 48
31 57
32 6
33 15
34 17
35 28
36 19
37 31
38 33
39 45
40 22
41 34
42 36
43 47
44 38
45 49
46 51
47 58
48 25
49 37
50 39
51 50
52 40
53 52
54 53
55 59
56 43
57 54
58 55
59 60
60 56
61 61
62 62
63 63
Fifth group of sequences (a criterion that preferentially considers a minimum code distance).
Sequence Q21, having a sequence length of 1024:
[0, 1, 2, 4, 8, 16, 32, 3, 5, 64, 6, 9, 17, 10, 18, 128, 12, 33, 256, 20, 34, 24, 65, 36, 7, 129, 66, 512, 11, 40, 68, 19, 13, 130, 48, 14, 72, 257, 21, 132, 35, 258, 26, 513, 80, 37, 25, 22, 136, 96, 260, 38, 514, 264, 67, 41, 144, 28, 69, 42, 516, 49, 160, 272, 70, 520, 288, 528, 131, 44, 544, 73, 192, 50, 74, 52, 15, 133, 320, 81, 23, 134, 76, 137, 82, 384, 56, 27, 97, 39, 259, 84, 138, 145, 261, 29, 43, 98, 515, 88, 140, 30, 146, 71, 262, 265, 517, 161, 45, 576, 518, 100, 51, 148, 521, 46, 75, 640, 266, 273, 522, 104, 162, 53, 193, 152, 77, 164, 268, 274, 54, 83, 530, 57, 112, 529, 524, 135, 78, 289, 194, 85, 276, 58, 168, 139, 99, 86, 60, 89, 768, 196, 290, 141, 101, 280, 545, 546, 532, 147, 176, 142, 90, 536, 292, 200, 263, 31, 149, 321, 322, 577, 102, 105, 296, 163, 92, 47, 150, 548, 208, 324, 385, 304, 267, 578, 106, 153, 386, 165, 55, 328, 113, 519, 552, 641, 154, 79, 108, 224, 269, 166, 523, 560, 580, 195, 277, 169, 275, 291, 59, 270, 114, 156, 87, 197, 116, 170, 61, 525, 531, 177, 278, 281, 526, 642, 293, 388, 91, 584, 769, 198, 172, 120, 201, 62, 143, 336, 282, 103, 178, 294, 93, 533, 644, 534, 547, 770, 392, 297, 592, 323, 202, 284, 151, 209, 180, 107, 325, 94, 537, 400, 298, 204, 352, 305, 155, 300, 210, 608, 648, 109, 184, 115, 167, 225, 326, 157, 110, 772, 549, 656, 538, 117, 212, 330, 171, 550, 329, 306, 226, 387, 308, 271, 579, 416, 216, 337, 158, 776, 118, 540, 553, 279, 332, 389, 173, 121, 199, 179, 228, 283, 122, 393, 174, 312, 672, 390, 554, 556, 203, 561, 181, 295, 448, 353, 338, 63, 581, 340, 285, 394, 232, 124, 354, 582, 784, 704, 527, 286, 182, 562, 643, 585, 205, 299, 211, 401, 185, 396, 240, 586, 645, 593, 535, 301, 402, 344, 206, 564, 800, 327, 356, 307, 95, 417, 213, 186, 404, 111, 539, 568, 594, 649, 771, 302, 832, 588, 646, 227, 360, 214, 188, 551, 609, 896, 331, 309, 418, 449, 217, 408, 229, 541, 159, 420, 596, 650, 773, 310, 333, 119, 368, 339, 391, 657, 313, 218, 542, 610, 334, 230, 233, 774, 658, 612, 175, 123, 450, 652, 341, 220, 557, 314, 555, 600, 583, 424, 395, 777, 673, 355, 287, 183, 234, 125, 342, 563, 674, 616, 558, 660, 778, 452, 397, 432, 316, 345, 241, 207, 785, 403, 357, 187, 587, 565, 664, 624, 780, 236, 126, 242, 398, 705, 346, 456, 358, 405, 303, 569, 595, 189, 786, 215, 676, 589, 566, 647, 361, 706, 244, 348, 419, 406, 311, 708, 219, 598, 601, 651, 611, 409, 680, 788, 362, 570, 597, 572, 464, 801, 590, 421, 802, 369, 792, 190, 602, 653, 248, 688, 231, 410, 364, 335, 422, 613, 659, 654, 315, 221, 370, 425, 235, 451, 480, 775, 412, 614, 343, 222, 317, 372, 543, 426, 453, 237, 559, 833, 804, 712, 834, 661, 808, 779, 617, 604, 433, 720, 816, 836, 347, 897, 243, 662, 454, 318, 675, 376, 428, 625, 238, 359, 567, 618, 665, 736, 898, 457, 399, 781, 591, 666, 678, 349, 434, 677, 840, 782, 626, 571, 620, 787, 363, 245, 458, 127, 407, 436, 465, 350, 246, 681, 460, 249, 599, 411, 365, 668, 707, 573, 789, 803, 790, 682, 440, 709, 466, 628, 371, 423, 366, 250, 413, 574, 468, 603, 481, 689, 793, 191, 373, 655, 900, 805, 427, 615, 710, 414, 252, 848, 684, 713, 605, 690, 632, 482, 794, 806, 472, 223, 663, 835, 904, 809, 714, 619, 796, 374, 429, 455, 692, 721, 837, 716, 864, 810, 606, 912, 722, 696, 377, 817, 435, 812, 484, 319, 430, 621, 838, 667, 239, 378, 459, 437, 627, 622, 488, 380, 461, 679, 841, 818, 724, 669, 496, 629, 928, 737, 899, 783, 738, 901, 842, 438, 467, 247, 820, 849, 683, 351, 791, 441, 728, 670, 462, 469, 442, 251, 367, 630, 740, 902, 711, 844, 850, 905, 685, 691, 824, 633, 483, 795, 744, 470, 852, 686, 444, 473, 253, 634, 485, 415, 375, 960, 865, 575, 807, 906, 715, 913, 693, 797, 866, 811, 717, 474, 254, 694, 723, 636, 486, 798, 607, 697, 489, 431, 379, 908, 752, 914, 856, 868, 839, 929, 813, 718, 819, 476, 916, 725, 698, 490, 739, 814, 843, 623, 497, 439, 381, 671, 463, 726, 930, 872, 821, 920, 700, 729, 492, 932, 961, 741, 903, 845, 498, 880, 382, 822, 851, 631, 443, 825, 730, 471, 445, 687, 635, 742, 846, 500, 745, 826, 732, 446, 962, 936, 255, 853, 504, 637, 907, 475, 746, 867, 487, 695, 799, 854, 828, 753, 857, 964, 909, 719, 477, 915, 869, 699, 748, 944, 638, 754, 491, 910, 858, 478, 815, 727, 917, 870, 493, 873, 701, 968, 383, 860, 756, 918, 931, 976, 499, 921, 874, 702, 823, 494, 731, 760, 881, 933, 501, 743, 922, 876, 847, 934, 827, 733, 502, 992, 882, 447, 963, 937, 747, 505, 855, 924, 734, 829, 884, 938, 506, 965, 749, 945, 966, 940, 969, 911, 946, 755, 888, 830, 859, 639, 871, 970, 750, 508, 948, 977, 757, 479, 919, 861, 875, 972, 978, 758, 862, 952, 761, 993, 923, 703, 495, 935, 877, 883, 980, 762, 925, 994, 878, 503, 885, 939, 984, 764, 996, 926, 735, 967, 886, 941, 507, 947, 889, 831, 1000, 942, 971, 751, 509, 949, 890, 973, 1008, 510, 950, 979, 759, 892, 863, 953, 974, 981, 954, 763, 995, 879, 982, 956, 985, 765, 997, 927, 887, 986, 766, 998, 1001, 943, 891, 988, 1002, 1009, 511, 951, 893, 1004, 975, 1010, 894, 955, 1012, 983, 957, 1016, 958, 987, 767, 999, 989, 1003, 990, 1005, 1011, 895, 1006, 1013, 1014, 1017, 959, 1018, 1020, 991, 1007, 1015, 1019, 1021, 1022, 1023]
TABLE Q21
having a sequence length of 1024:
Reliability Polarized
or sequence channel
number of sequence
reliability number
0 0
1 1
2 2
3 4
4 8
5 16
6 32
7 3
8 5
9 64
10 6
11 9
12 17
13 10
14 18
15 128
16 12
17 33
18 256
19 20
20 34
21 24
22 65
23 36
24 7
25 129
26 66
27 512
28 11
29 40
30 68
31 19
32 13
33 130
34 48
35 14
36 72
37 257
38 21
39 132
40 35
41 258
42 26
43 513
44 80
45 37
46 25
47 22
48 136
49 96
50 260
51 38
52 514
53 264
54 67
55 41
56 144
57 28
58 69
59 42
60 516
61 49
62 160
63 272
64 70
65 520
66 288
67 528
68 131
69 44
70 544
71 73
72 192
73 50
74 74
75 52
76 15
77 133
78 320
79 81
80 23
81 134
82 76
83 137
84 82
85 384
86 56
87 27
88 97
89 39
90 259
91 84
92 138
93 145
94 261
95 29
96 43
97 98
98 515
99 88
100 140
101 30
102 146
103 71
104 262
105 265
106 517
107 161
108 45
109 576
110 518
111 100
112 51
113 148
114 521
115 46
116 75
117 640
118 266
119 273
120 522
121 104
122 162
123 53
124 193
125 152
126 77
127 164
128 268
129 274
130 54
131 83
132 530
133 57
134 11
135 529
136 524
137 135
138 78
139 289
140 194
141 85
142 276
143 58
144 168
145 139
146 99
147 86
148 60
149 89
150 768
151 196
152 290
153 141
154 101
155 280
156 545
157 546
158 532
159 147
160 176
161 142
162 90
163 536
164 292
165 200
166 263
167 31
168 149
169 321
170 322
171 577
172 102
173 105
174 296
175 163
176 92
177 47
178 150
179 548
180 208
181 324
182 385
183 304
184 267
185 578
186 106
187 153
188 386
189 165
190 55
191 328
192 113
193 519
194 552
195 641
196 154
197 79
198 108
199 224
200 269
201 166
202 523
203 560
204 580
205 195
206 277
207 169
208 275
209 291
210 59
211 270
212 114
213 156
214 87
215 197
216 116
217 170
218 61
219 525
220 531
221 177
222 278
223 281
224 526
225 642
226 293
227 388
228 91
229 584
230 769
231 198
232 172
233 120
234 201
235 62
236 143
237 336
238 282
239 103
240 178
241 294
242 93
243 533
244 644
245 534
246 547
247 770
248 392
249 297
250 592
251 323
252 202
253 284
254 151
255 209
256 180
257 107
258 325
259 94
260 537
261 400
262 298
263 204
264 352
265 305
266 155
267 300
268 210
269 608
270 648
271 109
272 184
273 115
274 167
275 225
276 326
277 157
278 110
279 772
280 549
281 656
282 538
283 117
284 212
285 330
286 171
287 550
288 329
289 306
290 226
291 387
292 308
293 271
294 579
295 416
296 216
297 337
298 158
299 776
300 118
301 540
302 553
303 279
304 332
305 389
306 173
307 121
308 199
309 179
310 228
311 283
312 122
313 393
314 174
315 312
316 672
317 390
318 554
319 556
320 203
321 561
322 181
323 295
324 448
325 353
326 338
327 63
328 581
329 340
330 285
331 394
332 232
333 124
334 354
335 582
336 784
337 704
338 527
339 286
340 182
341 562
342 643
343 585
344 205
345 299
346 211
347 401
348 185
349 396
350 240
351 586
352 645
353 593
354 535
355 301
356 402
357 344
358 206
359 564
360 800
361 327
362 356
363 307
364 95
365 417
366 213
367 186
368 404
369 111
370 539
371 568
372 594
373 649
374 771
375 302
376 832
377 588
378 646
379 227
380 360
381 214
382 188
383 551
384 609
385 896
386 331
387 309
388 418
389 449
390 217
391 408
392 229
393 541
394 159
395 420
396 596
397 650
398 773
399 310
400 333
401 119
402 368
403 339
404 391
405 657
406 313
407 218
408 542
409 610
410 334
411 230
412 233
413 774
414 658
415 612
416 175
417 123
418 450
419 652
420 341
421 220
422 557
423 314
424 555
425 600
426 583
427 424
428 395
429 777
430 673
431 355
432 287
433 183
434 234
435 125
436 342
437 563
438 674
439 616
440 558
441 660
442 778
443 452
444 397
445 432
446 316
447 345
448 241
449 207
450 785
451 403
452 357
453 187
454 587
455 565
456 664
457 624
458 780
459 236
460 126
461 242
462 398
463 705
464 346
465 456
466 358
467 405
468 303
469 569
470 595
471 189
472 786
473 215
474 676
475 589
476 566
477 647
478 361
479 706
480 244
481 348
482 419
483 406
484 311
485 219
486 219
487 498
488 601
489 651
490 611
491 409
492 680
493 788
494 362
495 570
496 597
497 572
498 464
499 801
500 590
501 421
502 802
503 369
504 792
505 190
506 602
507 653
508 248
509 688
510 231
511 410
512 364
513 335
514 422
515 613
516 659
517 654
518 315
519 221
520 370
521 425
522 235
523 451
524 480
525 775
526 412
527 614
528 343
529 222
530 317
531 372
532 543
533 426
534 453
535 237
536 559
537 833
538 804
539 712
540 834
541 661
542 808
543 779
544 617
545 604
546 433
547 720
548 816
549 836
550 347
551 897
552 243
553 662
554 454
555 318
556 675
557 376
558 428
559 625
560 238
561 359
562 567
563 618
564 665
565 736
566 898
567 457
568 399
569 781
570 591
571 666
572 678
573 349
574 434
575 677
576 840
577 782
578 626
579 571
580 620
581 787
582 363
583 345
584 458
585 127
586 407
587 436
588 465
589 350
590 246
591 681
592 460
593 249
594 599
595 411
596 365
597 668
598 707
599 573
600 789
601 803
602 790
603 682
604 440
605 709
606 466
607 628
608 371
609 423
610 366
611 250
612 413
614 468
615 603
616 481
617 689
618 793
619 191
620 373
621 655
622 900
623 805
624 427
625 615
626 710
627 414
628 252
629 848
630 684
631 713
632 605
633 690
634 632
635 482
636 795
637 806
638 472
639 223
640 663
641 835
642 904
643 809
644 714
645 619
646 796
647 374
648 429
649 455
650 692
651 721
652 837
653 716
654 864
655 810
656 606
657 912
658 722
659 696
660 377
661 817
662 435
663 812
664 484
665 319
666 430
667 621
668 838
669 667
670 239
671 378
672 459
673 437
674 627
675 622
676 488
677 380
678 461
679 679
680 841
681 818
682 724
683 669
684 496
685 629
686 928
687 727
688 899
689 783
690 728
691 901
692 842
693 438
694 467
695 247
696 820
697 849
698 683
699 351
700 791
701 441
702 728
703 670
704 462
705 469
706 442
707 251
708 367
709 630
710 740
711 902
712 711
713 844
714 850
715 905
716 685
717 691
718 824
719 633
720 483
721 295
722 744
723 470
724 852
725 686
726 444
727 473
728 253
729 634
730 485
731 415
732 375
733 960
734 895
735 575
736 807
737 906
738 715
739 913
740 693
741 797
742 866
743 811
744 717
745 474
746 254
747 694
748 723
749 636
750 486
751 798
752 607
753 697
754 489
755 431
756 379
757 908
758 752
759 914
760 856
761 868
762 839
763 929
764 813
765 718
766 819
767 476
768 916
769 725
770 698
771 490
772 739
773 814
774 843
775 623
776 497
777 439
778 381
779 671
780 463
781 726
782 930
783 872
784 821
785 920
786 700
787 729
788 492
789 932
790 961
791 741
792 903
793 845
794 498
795 880
796 382
797 822
798 851
799 631
800 443
801 825
802 730
803 471
804 445
805 687
806 635
807 742
808 846
809 500
810 745
811 826
812 732
813 446
814 962
815 936
816 255
817 853
818 504
819 637
820 907
821 475
822 746
823 867
824 487
825 695
826 799
827 854
828 828
829 753
830 857
831 964
832 909
833 719
834 477
835 915
836 869
837 699
838 748
839 944
840 638
841 754
842 491
843 910
844 858
845 478
846 815
847 727
848 917
849 870
850 493
851 873
852 701
853 968
854 383
855 860
856 756
857 918
858 931
859 976
860 499
861 921
862 874
863 702
864 823
865 494
866 731
867 760
868 881
869 933
870 501
871 743
872 922
873 876
874 847
875 934
876 827
877 733
878 502
879 992
880 882
881 447
882 963
883 937
884 747
885 505
886 855
887 924
888 724
889 829
890 884
891 938
892 506
893 965
894 729
895 945
896 966
897 940
898 969
899 911
900 946
901 755
902 888
903 830
904 859
905 639
906 871
907 970
908 750
909 508
910 948
911 977
912 757
913 479
914 919
915 861
916 875
917 972
918 978
919 758
920 862
921 852
922 761
923 993
924 923
925 703
926 495
927 935
928 877
929 883
930 980
931 762
932 925
933 994
934 878
935 503
936 885
937 939
938 984
939 764
940 996
941 926
942 735
943 967
944 886
945 941
946 504
947 947
948 889
949 831
950 1000
951 942
952 971
953 751
954 509
955 949
956 890
957 973
958 1008
959 510
960 950
961 979
962 759
963 892
964 863
965 853
966 974
967 981
968 954
969 763
970 995
971 879
972 982
973 956
974 985
975 765
976 997
977 927
978 887
979 986
980 766
981 998
982 1001
983 943
984 891
985 988
986 1002
987 1009
988 511
989 951
990 893
991 1004
992 975
993 1010
994 894
995 955
996 1012
997 983
998 957
999 1016
1000 958
1001 987
1002 767
1003 999
1004 989
1005 1003
1006 990
1007 1005
1008 1011
1009 895
1010 1006
1011 1013
1012 1014
1013 1017
1014 959
1015 1018
1016 1020
1017 991
1018 1007
1019 1015
1020 1019
1021 1021
1022 1022
1023 1023
Sequence Q22, having a sequence length of 512:
[0, 1, 2, 4, 8, 16, 32, 3, 5, 64, 6, 9, 17, 10, 18, 128, 12, 33, 256, 20, 34, 24, 65, 36, 7, 129, 66, 11, 40, 68, 19, 13, 130, 48, 14, 72, 257, 21, 132, 35, 258, 26, 80, 37, 25, 22, 136, 96, 260, 38, 264, 67, 41, 144, 28, 69, 42, 49, 160, 272, 70, 288, 131, 44, 73, 192, 50, 74, 52, 15, 133, 320, 81, 23, 134, 76, 137, 82, 384, 56, 27, 97, 39, 259, 84, 138, 145, 261, 29, 43, 98, 88, 140, 30, 146, 71, 262, 265, 161, 45, 100, 51, 148, 46, 75, 266, 273, 104, 162, 53, 193, 152, 77, 164, 268, 274, 54, 83, 57, 112, 135, 78, 289, 194, 85, 276, 58, 168, 139, 99, 86, 60, 89, 196, 290, 141, 101, 280, 147, 176, 142, 90, 292, 200, 263, 31, 149, 321, 322, 102, 105, 296, 163, 92, 47, 150, 208, 324, 385, 304, 267, 106, 153, 386, 165, 55, 328, 113, 154, 79, 108, 224, 269, 166, 195, 277, 169, 275, 291, 59, 270, 114, 156, 87, 197, 116, 170, 61, 177, 278, 281, 293, 388, 91, 198, 172, 120, 201, 62, 143, 336, 282, 103, 178, 294, 93, 392, 297, 323, 202, 284, 151, 209, 180, 107, 325, 94, 400, 298, 204, 352, 305, 155, 300, 210, 109, 184, 115, 167, 225, 326, 157, 110, 117, 212, 330, 171, 329, 306, 226, 387, 308, 271, 416, 216, 337, 158, 118, 279, 332, 389, 173, 121, 199, 179, 228, 283, 122, 393, 174, 312, 390, 203, 181, 295, 448, 353, 338, 63, 340, 285, 394, 232, 124, 354, 286, 182, 205, 299, 211, 401, 185, 396, 240, 301, 402, 344, 206, 327, 356, 307, 95, 417, 213, 186, 404, 111, 302, 227, 360, 214, 188, 331, 309, 418, 449, 217, 408, 229, 159, 420, 310, 333, 119, 368, 339, 391, 313, 218, 334, 230, 233, 175, 123, 450, 341, 220, 314, 424, 395, 355, 287, 183, 234, 125, 342, 452, 397, 432, 316, 345, 241, 207, 403, 357, 187, 236, 126, 242, 398, 346, 456, 358, 405, 303, 189, 215, 361, 244, 348, 419, 406, 311, 219, 409, 362, 464, 421, 369, 190, 248, 231, 410, 364, 335, 422, 315, 221, 370, 425, 235, 451, 480, 412, 343, 222, 317, 372, 426, 453, 237, 433, 347, 243, 454, 318, 376, 428, 238, 359, 457, 399, 349, 434, 363, 245, 458, 127, 407, 436, 465, 350, 246, 460, 249, 411, 365, 440, 466, 371, 423, 366, 250, 413, 468, 481, 191, 373, 427, 414, 252, 482, 472, 223, 374, 429, 455, 377, 435, 484, 319, 430, 239, 378, 459, 437, 488, 380, 461, 496, 438, 467, 247, 351, 441, 462, 469, 442, 251, 367, 483, 470, 444, 473, 253, 485, 415, 375, 474, 254, 486, 489, 431, 379, 476, 490, 497, 439, 381, 463, 492, 498, 382, 443, 471, 445, 500, 446, 255, 504, 475, 487, 477, 491, 478, 493, 383, 499, 494, 501, 502, 447, 505, 506, 508, 479, 495, 503, 507, 509, 510, 511]
TABLE Q22
having a sequence length of 512:
Reliability Polarized
or sequence channel
number of sequence
reliability number
0 0
1 1
2 2
3 4
4 8
5 16
6 32
7 3
8 5
9 64
10 6
11 9
12 17
13 10
14 18
15 128
16 12
17 33
18 256
19 20
20 34
21 24
22 65
23 36
24 7
25 129
26 66
27 11
28 40
29 68
30 19
31 13
32 130
33 48
34 14
35 72
36 257
37 21
38 132
39 35
40 258
41 26
42 80
43 37
44 25
45 22
46 136
47 96
48 260
49 38
50 264
51 67
52 41
53 144
54 28
55 69
56 42
57 49
58 160
59 272
60 70
61 288
62 131
63 44
64 73
65 192
66 50
67 74
68 52
69 15
70 133
71 320
72 81
73 23
74 134
75 76
76 137
77 82
78 384
79 56
80 27
81 97
82 39
83 259
84 148
85 138
86 145
87 261
88 29
89 43
90 98
91 88
92 140
93 30
94 146
95 71
96 262
97 265
98 161
99 45
100 100
101 51
102 148
103 46
104 75
105 266
106 273
107 104
108 162
109 53
110 193
111 152
112 77
113 164
114 268
115 274
116 54
117 83
118 57
119 112
120 135
121 78
122 289
123 194
124 85
125 276
126 58
127 168
128 139
129 99
130 86
131 60
132 89
133 196
134 290
135 141
136 101
137 280
138 147
139 176
140 142
141 90
142 292
143 200
144 263
145 31
146 149
147 321
148 322
149 102
150 105
151 296
152 163
153 92
154 47
155 150
156 208
157 324
158 385
159 304
160 267
161 106
162 153
163 386
164 165
165 55
166 328
167 113
168 154
169 240
170 108
171 224
172 269
173 166
174 195
175 277
176 169
177 275
178 291
179 59
180 270
181 114
182 156
183 87
184 197
185 116
186 170
187 61
188 177
189 278
190 281
191 293
192 388
193 91
194 198
195 172
196 120
197 201
198 62
199 143
200 336
201 282
202 103
203 178
204 294
205 93
206 392
207 297
208 323
209 202
210 284
211 151
212 209
213 180
214 107
215 325
216 94
217 400
218 298
219 204
220 352
221 305
222 155
223 300
224 210
225 109
226 184
227 115
228 167
229 225
230 326
231 157
232 110
233 117
234 212
235 330
236 171
237 329
238 306
239 226
240 387
241 308
242 271
243 416
244 216
245 337
246 158
247 118
248 279
249 332
250 389
251 173
252 121
253 199
254 179
255 228
256 283
257 122
258 393
259 174
260 312
261 390
262 203
263 181
264 295
265 448
266 353
267 338
268 63
269 340
270 285
271 394
272 232
273 124
274 354
275 286
276 182
277 205
278 299
279 211
280 401
281 185
282 396
283 240
284 301
285 402
286 344
287 206
288 327
289 356
290 307
291 95
292 417
293 213
294 186
295 404
296 111
297 302
298 227
299 360
300 214
301 188
302 331
303 309
304 418
305 449
306 217
307 408
308 229
309 159
310 420
311 310
312 333
313 119
314 368
315 339
316 391
317 313
318 218
319 334
320 230
321 233
322 175
323 123
324 450
325 341
326 220
327 314
328 424
329 395
330 355
331 287
332 183
333 234
334 125
335 342
336 452
337 397
338 432
339 316
340 345
341 241
342 207
343 403
344 357
345 187
346 236
347 126
348 242
349 398
350 346
351 456
352 358
353 405
354 303
355 189
356 215
357 361
358 244
359 248
360 419
361 406
362 311
363 219
364 409
365 362
366 464
367 421
368 369
369 190
370 248
371 231
372 410
373 264
374 335
375 422
376 315
377 221
378 370
379 425
380 435
381 451
382 480
383 412
384 343
385 222
386 317
387 372
388 426
389 453
390 237
391 433
392 347
393 243
394 454
395 318
396 376
397 428
398 238
399 359
400 457
401 399
402 349
403 434
404 363
405 245
406 458
407 127
408 407
409 436
410 465
411 350
412 246
413 460
414 249
415 411
416 365
417 440
418 466
419 371
420 423
421 366
422 250
423 413
424 468
425 481
426 191
427 373
428 427
429 414
430 252
431 482
432 472
433 223
434 374
435 429
436 455
437 377
438 435
439 484
440 319
441 430
442 239
443 378
444 459
445 437
446 488
447 380
448 461
449 496
450 438
451 467
452 247
453 453
454 441
455 462
456 469
457 442
458 251
459 367
460 483
461 470
462 444
463 473
464 253
465 485
466 415
467 375
468 474
469 254
470 486
471 489
472 431
473 379
474 476
475 490
476 497
477 439
478 381
479 463
480 492
481 498
482 382
483 443
484 471
485 445
486 500
487 446
488 255
489 504
490 475
491 487
492 477
493 491
494 478
495 493
496 383
497 499
498 494
499 501
500 502
501 447
502 505
503 506
504 508
505 479
506 495
507 503
508 507
509 509
510 510
511 511
Sequence Q23, having a sequence length of 256:
[0, 1, 2, 4, 8, 16, 32, 3, 5, 64, 6, 9, 17, 10, 18, 128, 12, 33, 20, 34, 24, 65, 36, 7, 129, 66, 11, 40, 68, 19, 13, 130, 48, 14, 72, 21, 132, 35, 26, 80, 37, 25, 22, 136, 96, 38, 67, 41, 144, 28, 69, 42, 49, 160, 70, 131, 44, 73, 192, 50, 74, 52, 15, 133, 81, 23, 134, 76, 137, 82, 56, 27, 97, 39, 84, 138, 145, 29, 43, 98, 88, 140, 30, 146, 71, 161, 45, 100, 51, 148, 46, 75, 104, 162, 53, 193, 152, 77, 164, 54, 83, 57, 112, 135, 78, 194, 85, 58, 168, 139, 99, 86, 60, 89, 196, 141, 101, 147, 176, 142, 90, 200, 31, 149, 102, 105, 163, 92, 47, 150, 208, 106, 153, 165, 55, 113, 154, 79, 108, 224, 166, 195, 169, 59, 114, 156, 87, 197, 116, 170, 61, 177, 91, 198, 172, 120, 201, 62, 143, 103, 178, 93, 202, 151, 209, 180, 107, 94, 204, 155, 210, 109, 184, 115, 167, 225, 157, 110, 117, 212, 171, 226, 216, 158, 118, 173, 121, 199, 179, 228, 122, 174, 203, 181, 63, 232, 124, 182, 205, 211, 185, 240, 206, 95, 213, 186, 111, 227, 214, 188, 217, 229, 159, 119, 218, 230, 233, 175, 123, 220, 183, 234, 125, 241, 207, 187, 236, 126, 242, 189, 215, 244, 219, 190, 248, 231, 221, 235, 222, 237, 243, 238, 245, 127, 246, 249, 250, 191, 252, 223, 239, 247, 251, 253, 254, 255]
TABLE Q23
having a sequence length of 256:
Reliability Polarized
or sequence channel
number of sequence
reliability number
0 0
1 1
2 2
3 4
4 8
5 16
6 32
7 3
8 5
9 64
10 6
11 9
12 17
13 10
14 18
15 128
16 12
17 33
18 20
19 34
20 24
21 65
22 36
23 7
24 129
25 66
26 11
27 40
28 68
29 19
30 13
31 130
32 48
33 14
34 72
35 21
36 132
37 35
38 26
39 80
40 37
41 25
42 22
43 136
44 96
45 38
46 67
47 41
48 144
49 28
50 69
51 42
52 49
53 160
54 70
55 131
56 44
57 73
58 192
59 50
60 74
61 52
62 15
63 133
64 81
65 23
66 134
67 76
68 137
69 82
70 56
71 27
72 97
73 39
74 84
75 138
76 145
77 29
78 43
79 98
80 88
81 140
82 30
83 146
84 71
85 161
86 45
87 100
88 51
89 148
90 46
91 75
92 104
93 162
94 53
95 193
96 152
97 77
98 164
99 54
100 83
101 57
102 112
103 135
104 78
105 194
106 85
107 58
108 168
109 139
110 99
111 86
112 60
113 89
114 196
115 141
116 101
117 147
118 176
119 142
120 90
121 200
122 31
123 149
124 102
125 105
126 163
127 92
128 47
129 150
130 208
131 106
132 153
133 165
134 55
135 113
136 154
137 79
138 108
139 224
140 166
141 195
142 169
143 59
144 114
145 156
146 87
147 197
148 116
149 170
150 61
151 177
152 91
153 198
154 172
155 120
156 201
157 62
158 143
159 103
160 178
161 93
162 202
163 151
164 209
165 180
166 107
197 94
168 204
169 155
170 210
171 109
172 184
173 115
174 167
175 225
176 157
177 110
178 117
179 212
180 171
181 226
182 216
183 158
184 118
185 173
186 121
187 199
188 179
189 228
190 122
191 174
192 203
193 181
194 63
195 232
196 124
197 182
198 205
199 211
200 185
201 240
202 206
203 95
204 213
205 186
206 111
207 227
208 214
209 188
210 217
211 229
212 159
213 119
214 218
215 230
216 233
217 175
218 123
219 220
220 183
221 234
222 125
223 241
224 207
225 187
226 236
227 126
228 242
229 189
230 215
231 244
232 219
233 190
234 248
235 231
236 221
237 235
238 222
239 237
240 243
241 238
242 245
243 127
244 246
245 249
246 250
247 191
248 252
249 223
250 239
251 247
252 251
253 253
254 254
255 255
Sequence Q24, having a sequence length of 128:
[0, 1, 2, 4, 8, 16, 32, 3, 5, 64, 6, 9, 17, 10, 18, 12, 33, 20, 34, 24, 65, 36, 7, 66, 11, 40, 68, 19, 13, 48, 14, 72, 21, 35, 26, 80, 37, 25, 22, 96, 38, 67, 41, 28, 69, 42, 49, 70, 44, 73, 50, 74, 52, 15, 81, 23, 76, 82, 56, 27, 97, 39, 84, 29, 43, 98, 88, 30, 71, 45, 100, 51, 46, 75, 104, 53, 77, 54, 83, 57, 112, 78, 85, 58, 99, 86, 60, 89, 101, 90, 31, 102, 105, 92, 47, 106, 55, 113, 79, 108, 59, 114, 87, 116, 61, 91, 120, 62, 103, 93, 107, 94, 109, 115, 110, 117, 118, 121, 122, 63, 124, 95, 111, 119, 123, 125, 126, 127]
TABLE Q24
having a sequence length of 128:
Reliability or Polarized
sequence channel
number of reliability sequence number
0 0
1 1
2 2
3 4
4 8
5 16
6 32
7 3
8 5
9 64
10 6
11 9
12 17
13 10
14 18
15 12
16 33
17 20
18 34
19 24
20 65
21 36
22 7
23 66
24 11
25 40
26 68
27 19
28 13
29 48
30 14
31 72
32 21
33 35
34 26
35 80
36 37
37 25
38 22
39 96
40 38
41 67
42 41
43 28
44 69
45 42
46 49
47 70
48 44
49 73
50 50
51 74
52 52
53 15
54 81
55 23
56 76
57 82
58 56
59 27
60 97
61 39
62 84
63 29
64 43
65 98
66 88
67 30
68 71
69 45
70 100
71 51
72 46
73 75
74 104
75 53
76 77
77 54
78 83
79 57
80 112
81 78
82 85
83 58
84 99
85 86
86 60
87 89
88 101
89 90
90 31
91 102
92 105
93 92
94 47
95 106
96 55
97 113
98 79
99 108
100 59
101 114
102 87
103 116
104 61
105 91
106 120
107 62
108 103
109 93
110 107
111 94
112 109
113 115
114 110
115 117
116 118
117 121
118 122
119 63
120 124
121 95
122 111
123 119
124 123
125 125
126 126
127 127
Sequence Q25, having a sequence length of 64:
[0, 1, 2, 4, 8, 16, 32, 3, 5, 6, 9, 17, 10, 18, 12, 33, 20, 34, 24, 36, 7, 11, 40, 19, 13, 48, 14, 21, 35, 26, 37, 25, 22, 38, 41, 28, 42, 49, 44, 50, 52, 15, 23, 56, 27, 39, 29, 43, 30, 45, 51, 46, 53, 54, 57, 58, 60, 31, 47, 55, 59, 61, 62, 63]
TABLE Q25
having a sequence length of 64:
Reliability or sequence Polarized channel
number of reliability sequence number
0 0
1 1
2 2
3 4
4 8
5 16
6 32
7 3
8 5
9 6
10 9
11 17
12 10
13 18
14 12
15 33
16 20
17 34
18 24
19 36
20 7
21 11
22 40
23 19
24 13
25 48
26 14
27 21
28 35
29 26
30 37
31 25
32 22
33 38
34 41
35 28
36 42
37 49
38 44
39 50
40 52
41 15
42 23
43 56
44 27
45 39
46 29
47 43
48 30
49 45
50 51
51 46
52 53
53 54
54 57
55 58
56 60
57 31
58 47
59 55
60 59
61 61
62 62
63 63
Sequence Z21, having a sequence length of 1024:
[0, 1, 2, 7, 3, 8, 10, 24, 4, 11, 13, 28, 16, 32, 35, 76, 5, 12, 14, 31, 19, 38, 47, 80, 21, 46, 42, 87, 57, 95, 101, 167, 6, 17, 20, 40, 23, 45, 51, 89, 29, 55, 59, 96, 69, 108, 115, 177, 34, 61, 73, 112, 75, 123, 130, 190, 86, 133, 143, 210, 148, 218, 235, 327, 9, 22, 26, 54, 30, 58, 64, 103, 36, 71, 74, 116, 82, 126, 138, 197, 44, 79, 84, 131, 91, 141, 147, 214, 99, 149, 162, 228, 176, 242, 259, 364, 49, 88, 97, 146, 111, 154, 172, 239, 121, 173, 186, 257, 198, 271, 278, 369, 134, 192, 212, 273, 216, 283, 300, 401, 233, 307, 312, 417, 333, 435, 460, 585, 15, 25, 33, 68, 39, 77, 81, 137, 48, 83, 92, 145, 100, 153, 161, 236, 56, 93, 102, 159, 113, 168, 178, 254, 125, 187, 196, 266, 213, 277, 298, 394, 62, 107, 122, 175, 127, 189, 201, 274, 144, 207, 217, 286, 232, 306, 314, 416, 160, 221, 240, 309, 256, 322, 340, 433, 272, 348, 367, 453, 382, 471, 505, 619, 72, 124, 140, 205, 151, 215, 231, 308, 165, 234, 252, 320, 263, 344, 358, 449, 180, 255, 268, 346, 284, 366, 381, 473, 296, 390, 407, 486, 421, 519, 529, 639, 199, 275, 290, 379, 310, 392, 411, 510, 332, 412, 434, 522, 459, 535, 560, 670, 350, 448, 461, 552, 480, 583, 590, 695, 508, 593, 611, 707, 628, 728, 746, 816, 18, 37, 41, 90, 50, 94, 104, 166, 53, 105, 118, 184, 128, 200, 211, 293, 63, 119, 129, 208, 142, 206, 222, 303, 155, 223, 238, 311, 253, 330, 339, 432, 66, 139, 152, 209, 164, 226, 241, 323, 174, 249, 262, 345, 267, 355, 375, 468, 183, 265, 289, 363, 292, 387, 399, 484, 315, 406, 423, 518, 446, 530, 555, 665, 78, 169, 170, 251, 181, 258, 276, 361, 191, 288, 285, 386, 304, 400, 410, 513, 237, 297, 326, 403, 329, 420, 436, 528, 357, 447, 464, 550, 481, 573, 589, 699, 264, 325, 334, 431, 362, 452, 466, 561, 380, 478, 494, 582, 512, 596, 610, 708, 402, 503, 520, 608, 531, 620, 647, 732, 557, 660, 671, 756, 677, 778, 796, 854, 85, 182, 188, 291, 227, 305, 317, 404, 248, 313, 331, 428, 349, 444, 462, 568, 261, 347, 356, 451, 368, 467, 483, 586, 391, 491, 511, 595, 526, 612, 627, 731, 295, 365, 388, 482, 395, 501, 514, 609, 427, 521, 533, 624, 558, 648, 666, 755, 445, 546, 574, 662, 587, 673, 693, 777, 604, 701, 706, 800, 726, 804, 813, 881, 324, 389, 418, 523, 443, 534, 554, 649, 465, 567, 584, 672, 592, 678, 704, 780, 498, 588, 606, 694, 614, 705, 723, 803, 638, 727, 745, 821, 767, 834, 845, 913, 524, 616, 635, 720, 664, 730, 750, 824, 676, 754, 771, 842, 788, 850, 865, 926, 684, 776, 794, 860, 809, 870, 878, 935, 818, 885, 892, 946, 909, 954, 959, 988, 27, 43, 52, 98, 60, 106, 110, 193, 65, 114, 120, 202, 136, 219, 224, 338, 67, 135, 132, 220, 158, 243, 245, 354, 163, 260, 282, 370, 301, 393, 408, 532, 70, 156, 157, 246, 179, 280, 287, 383, 194, 302, 318, 424, 319, 422, 440, 536, 203, 321, 341, 437, 359, 455, 476, 562, 371, 469, 495, 579, 497, 599, 613, 735, 109, 171, 185, 294, 204, 328, 335, 426, 229, 343, 351, 454, 377, 475, 500, 570, 250, 353, 372, 470, 396, 496, 487, 594, 425, 488, 506, 615, 545, 632, 656, 752, 269, 384, 409, 490, 415, 515, 527, 625, 439, 544, 563, 645, 580, 667, 675, 775, 457, 559, 578, 674, 607, 685, 709, 799, 634, 719, 729, 806, 749, 819, 840, 905, 117, 195, 225, 342, 244, 352, 378, 477, 270, 373, 397, 489, 419, 507, 517, 621, 281, 405, 414, 516, 441, 541, 553, 640, 456, 564, 571, 669, 597, 683, 703, 779, 316, 430, 438, 556, 474, 575, 572, 679, 492, 591, 603, 698, 630, 716, 725, 805, 509, 617, 633, 717, 650, 740, 747, 825, 659, 753, 770, 837, 786, 852, 863, 925, 337, 463, 479, 598, 485, 605, 626, 712, 539, 631, 644, 738, 653, 744, 765, 833, 547, 651, 658, 748, 682, 769, 781, 847, 702, 787, 802, 866, 812, 877, 888, 942, 565, 687, 690, 772, 710, 791, 807, 871, 722, 810, 822, 884, 838, 894, 908, 953, 758, 829, 841, 901, 856, 912, 919, 962, 867, 922, 931, 969, 939, 975, 980, 1002, 150, 230, 247, 374, 279, 398, 413, 525, 299, 429, 442, 543, 458, 569, 577, 689, 336, 450, 472, 581, 493, 600, 602, 700, 504, 618, 636, 721, 646, 741, 751, 826, 360, 499, 502, 601, 538, 623, 637, 736, 542, 643, 655, 743, 663, 764, 773, 846, 548, 661, 681, 766, 696, 784, 797, 864, 718, 801, 811, 876, 828, 889, 903, 949, 376, 537, 540, 641, 549, 652, 668, 762, 576, 680, 692, 774, 713, 793, 808, 874, 629, 697, 714, 798, 724, 817, 827, 886, 760, 830, 844, 904, 855, 915, 920, 964, 654, 734, 742, 823, 761, 836, 849, 906, 783, 851, 862, 916, 873, 928, 934, 971, 795, 868, 880, 929, 890, 936, 944, 978, 902, 948, 956, 984, 963, 990, 994, 1009, 385, 551, 566, 688, 622, 691, 711, 792, 642, 715, 737, 820, 757, 832, 843, 899, 657, 739, 759, 835, 768, 848, 857, 914, 785, 861, 872, 924, 887, 932, 941, 977, 686, 763, 782, 858, 789, 869, 875, 927, 815, 883, 891, 937, 897, 945, 951, 983, 839, 895, 900, 947, 910, 955, 960, 989, 921, 965, 968, 995, 973, 998, 1000, 1014, 733, 790, 814, 882, 831, 893, 896, 943, 853, 898, 907, 952, 917, 957, 966, 992, 859, 911, 918, 961, 930, 967, 972, 997, 938, 974, 979, 1001, 985, 1004, 1006, 1017, 879, 923, 933, 970, 940, 976, 981, 1003, 950, 982, 986, 1005, 991, 1007, 1010, 1018, 958, 987, 993, 1008, 996, 1011, 1012, 1019, 999, 1013, 1015, 1020, 1016, 1021, 1022, 1023]
TABLE Z21
having a sequence length of 1024:
Polarized channel Reliability or sequence
sequence number number of reliability
0 0
1 1
2 2
3 7
4 3
5 8
6 10
7 24
8 4
9 11
10 13
11 28
12 16
13 32
14 35
15 76
16 5
17 12
18 14
19 31
20 19
21 38
22 47
23 80
24 21
25 46
26 42
27 87
28 57
29 95
30 101
31 167
32 6
33 17
34 20
35 40
36 23
37 45
38 51
39 89
40 29
41 55
42 59
43 96
44 69
45 108
46 115
47 177
48 34
49 61
50 73
51 112
52 75
53 123
54 130
55 190
56 86
57 133
58 143
59 210
60 148
61 218
62 235
63 327
64 9
65 22
66 26
67 54
68 30
69 58
70 64
71 103
72 36
73 71
74 74
75 116
76 82
77 126
78 138
79 197
80 44
81 79
82 84
83 131
84 91
85 141
86 147
87 214
88 99
89 149
90 162
91 228
92 176
93 242
94 259
95 364
96 49
97 88
98 97
99 146
100 111
101 154
102 172
103 239
104 121
105 173
106 186
107 257
108 198
109 271
110 278
111 369
112 134
113 192
114 212
115 273
116 216
117 283
118 300
119 401
120 233
121 307
122 312
123 417
124 333
125 435
126 460
127 585
128 15
129 25
130 33
131 68
132 39
133 77
134 81
135 137
136 48
137 83
138 92
139 145
140 100
141 153
142 161
143 236
144 56
145 93
146 102
147 159
148 113
149 168
150 178
151 254
152 125
153 187
154 196
155 266
156 213
157 277
158 298
159 394
160 62
161 107
162 122
163 175
164 127
165 189
166 201
167 274
168 144
169 207
170 217
171 286
172 232
173 306
174 314
175 416
176 160
177 221
178 240
179 309
180 256
181 322
182 340
183 433
184 272
185 348
186 367
187 453
188 382
189 471
190 505
191 619
192 72
193 124
194 140
195 205
196 151
197 215
198 231
199 308
200 165
201 234
202 252
203 320
204 263
205 344
206 358
207 449
208 180
209 255
210 268
211 346
212 284
213 366
214 381
215 473
216 296
217 390
218 407
219 486
220 421
221 519
222 529
223 639
224 199
225 275
226 290
227 379
228 310
229 392
230 411
231 510
232 332
233 412
234 434
235 522
236 459
237 535
238 560
239 670
240 350
241 448
242 461
243 552
244 480
245 583
246 590
247 695
248 508
249 593
250 611
251 707
252 628
253 728
254 746
255 816
256 18
257 37
258 41
259 90
260 50
261 94
262 104
263 166
264 53
265 105
266 118
267 184
268 128
269 200
270 211
271 293
272 63
273 119
274 129
275 208
276 142
277 206
278 222
279 303
280 155
281 223
282 238
283 311
284 253
285 330
286 339
287 432
288 66
289 139
290 152
291 209
292 164
293 226
294 241
295 323
296 174
297 249
298 262
299 345
300 267
301 355
302 375
303 468
304 183
305 265
306 289
307 363
308 292
309 387
310 399
311 484
312 315
313 406
314 423
315 518
316 446
317 530
318 555
319 665
320 78
321 169
322 170
323 251
324 181
325 258
326 276
327 361
328 191
329 288
330 285
331 386
332 304
333 400
334 410
335 513
336 237
337 297
338 326
339 403
340 329
341 420
342 436
343 528
344 357
345 447
346 464
347 550
348 481
349 573
350 589
351 699
352 264
353 325
354 334
355 431
356 362
357 452
358 466
359 561
360 380
361 478
362 494
363 582
364 512
365 596
366 610
367 708
368 402
369 503
370 520
371 608
372 531
373 620
374 647
375 732
376 557
377 660
378 671
379 756
380 677
381 778
382 796
383 854
384 85
385 182
386 188
387 291
388 227
389 305
390 317
391 404
392 248
393 313
394 331
395 428
396 349
397 444
398 462
399 568
400 261
401 347
402 356
403 451
404 368
405 467
406 483
407 586
408 391
409 491
410 511
411 595
412 526
413 612
414 627
415 731
416 295
417 365
418 388
419 482
420 395
421 501
422 514
423 609
424 427
425 521
426 533
427 624
428 558
429 648
430 666
431 755
432 445
433 546
434 574
435 662
436 587
437 673
438 693
439 777
440 604
441 701
442 706
443 800
444 726
445 804
446 813
447 881
448 324
449 389
450 418
451 523
452 443
453 534
454 554
455 649
456 465
457 567
458 584
459 672
460 592
461 678
462 704
463 780
464 498
465 588
466 606
467 694
468 614
469 705
470 723
471 803
472 638
473 727
474 745
475 821
476 767
477 834
478 845
479 913
480 524
481 616
482 635
483 720
484 664
485 730
486 750
487 824
488 676
489 754
490 771
491 842
492 788
493 850
494 865
495 926
496 684
497 776
498 794
499 860
500 809
501 870
502 878
503 935
504 818
505 885
506 892
507 946
508 909
509 954
510 959
511 988
512 27
513 43
514 52
515 98
516 60
517 106
518 110
519 193
520 65
521 114
522 120
523 202
524 136
525 219
526 224
527 338
528 67
529 135
530 132
531 220
532 158
533 243
534 245
535 354
536 163
537 260
538 282
539 370
540 301
541 393
542 408
543 532
544 70
545 156
546 157
547 246
548 179
549 280
550 287
551 383
552 194
553 302
554 318
555 424
556 319
557 422
558 440
559 536
560 203
561 321
562 341
563 437
564 359
565 455
566 476
567 562
568 371
569 469
570 495
571 579
572 497
573 599
574 613
575 735
576 109
577 171
578 185
579 294
580 204
581 328
582 335
583 426
584 229
585 343
586 351
587 454
588 377
589 475
590 500
591 570
592 250
593 353
594 372
595 470
596 396
597 496
598 487
599 594
600 425
601 488
602 506
603 615
604 545
605 632
606 656
607 752
608 269
609 384
610 409
611 490
612 415
613 515
614 527
615 625
616 439
617 544
618 563
619 645
620 580
621 667
622 675
623 775
624 457
625 559
626 578
627 674
628 607
629 685
630 709
631 799
632 634
633 719
634 729
635 806
636 749
637 819
638 840
639 905
640 117
641 195
642 225
643 342
644 244
645 352
646 378
647 477
648 270
649 373
650 397
651 489
652 419
653 507
654 517
655 621
656 281
657 405
658 414
659 516
660 441
661 541
662 553
663 640
664 456
665 564
666 571
667 669
668 597
669 683
670 703
671 779
672 316
673 430
674 438
675 556
676 474
677 575
678 572
679 679
680 492
681 591
682 603
683 698
684 630
685 716
686 725
687 805
688 509
689 617
690 633
691 717
692 650
693 740
694 747
695 825
696 659
697 753
698 770
699 837
700 786
701 852
702 863
703 925
704 337
705 463
706 479
707 598
708 485
709 605
710 626
711 712
712 539
713 631
714 644
715 738
716 653
717 744
718 765
719 833
720 547
721 651
722 658
723 748
724 682
725 769
726 781
727 847
728 702
729 787
730 802
731 866
732 812
733 877
734 888
735 942
736 565
737 687
738 690
739 772
740 710
741 791
742 807
743 871
744 722
745 810
746 822
747 884
748 838
749 894
750 908
751 953
752 758
753 829
754 841
755 901
756 856
757 912
758 919
759 962
760 867
761 922
762 931
763 969
764 939
765 975
766 980
767 1002
768 150
769 230
770 247
771 374
772 279
773 398
774 413
775 525
776 299
777 429
778 442
779 543
780 458
781 569
782 577
783 689
784 336
785 450
786 472
787 581
788 493
789 600
790 602
791 700
792 504
793 618
794 636
795 721
796 646
797 741
798 751
799 826
800 360
801 499
802 502
803 601
804 538
805 623
806 637
807 736
808 542
809 643
810 655
811 743
812 663
813 764
814 773
815 846
816 548
817 661
818 681
819 766
820 696
821 784
822 797
823 864
824 718
825 801
826 811
827 876
828 828
829 889
830 903
831 949
832 376
833 537
834 540
835 641
836 549
837 652
838 668
839 762
840 576
841 680
842 692
843 774
844 713
845 793
846 808
847 874
848 629
849 697
850 714
851 798
852 724
853 817
854 827
855 886
856 760
857 830
858 844
859 904
860 855
861 915
862 920
863 964
864 654
865 734
866 742
867 823
868 761
869 836
870 849
871 906
872 783
873 851
874 862
875 916
876 873
877 928
878 934
879 971
880 795
881 868
882 880
883 929
884 890
885 936
886 944
887 978
888 902
889 948
890 956
891 984
892 963
893 990
894 994
895 1009
896 385
897 551
898 566
899 688
900 622
901 691
902 711
903 792
904 642
905 715
906 737
907 820
908 757
909 832
910 843
911 899
912 657
913 739
914 759
915 835
916 768
917 848
918 857
919 914
920 785
921 861
922 872
923 924
924 887
925 932
926 941
927 977
928 686
929 763
930 782
931 858
932 789
933 869
934 875
935 927
936 815
937 883
938 891
939 937
940 897
941 945
942 951
943 983
944 839
945 895
946 900
947 947
948 910
949 955
950 960
951 989
952 921
953 965
954 968
955 995
956 973
957 998
958 1000
959 1014
960 733
961 790
962 814
963 882
964 831
965 893
966 896
967 943
968 853
969 898
970 907
971 952
972 917
973 957
974 966
975 992
976 859
977 911
978 918
979 961
980 930
981 967
982 972
983 997
984 938
985 974
986 979
987 1001
988 985
989 1004
990 1006
991 1017
992 879
993 923
994 933
995 970
996 940
997 976
998 981
999 1003
1000 950
1001 982
1002 986
1003 1005
1004 991
1005 1007
1006 1010
1007 1018
1008 958
1009 987
1010 993
1011 1008
1012 996
1013 1011
1014 1012
1015 1019
1016 999
1017 1013
1018 1015
1019 1020
1020 1016
1021 1021
1022 1022
1023 1023
Sequence Z22, having a sequence length of 512:
[0, 1, 2, 7, 3, 8, 10, 24, 4, 11, 13, 27, 16, 31, 34, 69, 5, 12, 14, 30, 19, 37, 45, 73, 21, 44, 41, 80, 54, 88, 93, 145, 6, 17, 20, 39, 23, 43, 49, 82, 28, 52, 56, 89, 63, 99, 103, 154, 33, 57, 66, 101, 68, 109, 116, 165, 79, 118, 126, 179, 131, 187, 198, 268, 9, 22, 26, 51, 29, 55, 60, 95, 35, 64, 67, 104, 75, 112, 121, 169, 42, 72, 77, 117, 84, 124, 130, 183, 91, 132, 141, 193, 153, 205, 216, 291, 47, 81, 90, 129, 100, 136, 149, 202, 107, 150, 161, 214, 170, 225, 232, 296, 119, 167, 181, 227, 185, 233, 247, 313, 196, 252, 257, 323, 273, 334, 347, 407, 15, 25, 32, 62, 38, 70, 74, 120, 46, 76, 85, 128, 92, 135, 140, 199, 53, 86, 94, 138, 102, 146, 155, 211, 111, 162, 168, 222, 182, 231, 246, 309, 58, 98, 108, 152, 113, 164, 173, 228, 127, 176, 186, 236, 195, 251, 259, 322, 139, 188, 203, 254, 213, 263, 276, 332, 226, 281, 294, 345, 301, 355, 369, 426, 65, 110, 123, 174, 133, 184, 194, 253, 143, 197, 209, 262, 219, 277, 287, 342, 156, 212, 224, 279, 234, 293, 300, 356, 244, 306, 318, 363, 326, 377, 385, 433, 171, 229, 239, 298, 255, 308, 320, 371, 272, 321, 333, 380, 346, 390, 398, 442, 283, 341, 348, 393, 358, 405, 412, 452, 370, 414, 422, 458, 430, 464, 469, 488, 18, 36, 40, 83, 48, 87, 96, 144, 50, 97, 105, 160, 114, 172, 180, 242, 59, 106, 115, 177, 125, 175, 189, 248, 137, 190, 201, 256, 210, 270, 275, 331, 61, 122, 134, 178, 142, 191, 204, 264, 151, 207, 218, 278, 223, 284, 297, 354, 159, 221, 238, 290, 241, 303, 311, 362, 260, 317, 327, 376, 339, 386, 395, 440, 71, 147, 148, 208, 157, 215, 230, 288, 166, 237, 235, 302, 249, 312, 319, 374, 200, 245, 267, 315, 269, 325, 335, 384, 286, 340, 350, 392, 359, 402, 411, 453, 220, 266, 274, 330, 289, 344, 352, 399, 299, 357, 365, 404, 373, 416, 421, 459, 314, 368, 378, 419, 387, 427, 434, 467, 396, 437, 443, 473, 447, 478, 482, 496, 78, 158, 163, 240, 192, 250, 261, 316, 206, 258, 271, 329, 282, 337, 349, 401, 217, 280, 285, 343, 295, 353, 361, 408, 307, 364, 372, 415, 383, 423, 429, 466, 243, 292, 304, 360, 310, 367, 375, 420, 328, 379, 388, 428, 397, 435, 441, 472, 338, 391, 403, 438, 409, 445, 450, 477, 417, 454, 457, 483, 462, 485, 487, 501, 265, 305, 324, 381, 336, 389, 394, 436, 351, 400, 406, 444, 413, 448, 455, 479, 366, 410, 418, 451, 424, 456, 461, 484, 432, 463, 468, 490, 474, 492, 494, 505, 382, 425, 431, 460, 439, 465, 470, 491, 446, 471, 475, 493, 480, 495, 498, 506, 449, 476, 481, 497, 486, 499, 500, 507, 489, 502, 503, 508, 504, 509, 510, 511]
TABLE Z22
having a sequence length of 512:
Polarized channel Reliability or sequence
sequence number number of reliability
0 0
1 1
2 2
3 7
4 3
5 8
6 10
7 24
8 4
9 11
10 13
11 27
12 16
13 31
14 34
15 69
16 5
17 12
18 14
19 30
20 19
21 37
22 45
23 73
24 21
25 44
26 41
27 80
28 54
29 88
30 93
31 145
32 6
33 17
34 20
35 39
36 23
37 43
38 49
39 82
40 28
41 52
42 56
43 89
44 63
45 99
46 103
47 154
48 33
49 57
50 66
51 101
52 68
53 109
54 116
55 165
56 79
57 118
58 126
59 179
60 131
61 187
62 198
63 268
64 9
65 22
66 26
67 51
68 29
69 55
70 60
71 95
72 35
73 64
74 67
75 104
76 75
77 112
78 121
79 169
80 42
81 72
82 77
83 117
84 84
85 124
86 130
87 183
88 91
89 132
90 141
91 193
92 153
93 205
94 216
95 291
96 47
97 81
98 90
99 129
100 100
101 136
102 149
103 202
104 107
105 150
106 161
107 214
108 170
109 225
110 232
111 296
112 119
113 167
114 181
115 227
116 185
117 233
118 247
119 313
120 196
121 252
122 257
123 323
124 273
125 334
126 347
127 407
128 15
129 25
130 32
131 62
132 38
133 70
134 74
135 120
136 46
137 76
138 85
139 128
140 92
141 135
142 140
143 199
144 53
145 86
146 94
147 138
148 102
149 146
150 155
151 211
152 111
153 162
154 168
155 222
156 182
157 231
158 246
159 309
160 58
161 98
162 108
163 152
164 113
165 164
166 173
167 228
168 127
169 176
170 186
171 236
172 195
173 251
174 259
175 322
176 139
177 188
178 203
179 254
180 213
181 263
182 276
183 332
184 226
185 281
186 294
187 345
188 301
189 355
190 369
191 426
192 65
193 110
194 123
195 174
196 133
197 184
198 194
199 253
200 143
201 197
202 209
203 262
204 219
205 277
206 287
207 342
208 156
209 212
210 224
211 279
212 234
213 293
214 300
215 356
216 244
217 306
218 318
219 363
220 326
221 377
222 385
223 433
224 171
225 229
226 239
227 298
228 255
229 308
230 320
231 371
232 272
233 321
234 333
235 380
236 346
237 390
238 398
239 442
240 283
241 341
242 348
243 393
244 358
245 405
246 412
247 452
248 370
249 414
250 422
251 458
252 430
253 464
254 469
255 488
256 18
257 36
258 40
259 83
260 48
261 87
262 96
263 144
264 50
265 97
266 105
267 160
268 114
269 172
270 180
271 242
272 59
273 106
274 115
275 177
276 125
277 175
278 189
279 248
280 137
281 190
282 201
283 256
284 210
285 270
286 275
287 331
288 61
289 122
290 134
291 178
292 142
293 191
294 204
295 264
296 151
297 207
298 218
299 278
300 223
301 284
302 297
303 354
304 159
305 221
306 238
307 290
308 241
309 303
310 311
311 362
312 260
313 317
314 327
315 376
316 339
317 386
318 395
319 440
320 71
321 147
322 148
323 208
324 157
325 215
326 230
327 288
328 166
329 237
330 235
331 302
332 249
333 312
334 319
335 374
336 200
337 245
338 267
339 315
340 269
341 325
342 335
343 384
344 286
345 340
346 350
347 392
348 359
349 402
350 411
351 453
352 220
353 266
354 274
355 330
356 289
357 344
358 352
359 399
360 299
361 357
362 365
363 404
364 373
365 416
366 421
367 459
368 314
369 368
370 378
371 419
372 387
373 427
374 434
375 467
376 396
377 437
378 443
379 473
380 447
381 478
382 482
383 496
384 78
385 158
386 163
387 240
388 192
389 250
390 261
391 316
392 206
393 258
394 271
395 329
396 282
397 337
398 349
399 401
400 217
401 280
402 285
403 343
404 295
405 353
406 361
407 408
408 307
409 364
410 372
411 415
412 383
413 423
414 429
415 466
416 243
417 292
418 304
419 360
420 310
421 367
422 375
423 420
424 328
425 379
426 388
427 428
428 397
429 435
430 441
431 472
432 338
433 391
434 403
435 438
436 409
437 445
438 450
439 477
440 417
441 454
442 457
443 483
444 462
445 485
446 487
447 501
448 265
449 305
450 324
451 381
452 336
453 389
454 394
455 436
456 351
457 400
458 406
459 444
460 413
461 448
462 455
463 479
464 366
465 410
466 418
467 451
468 424
469 456
470 461
471 484
472 432
473 463
474 468
475 490
476 474
477 492
478 494
479 505
480 382
481 425
482 431
483 460
484 439
485 465
486 470
487 491
488 446
489 471
490 475
491 493
492 480
493 495
494 498
495 506
496 449
497 476
498 481
499 497
500 486
501 499
502 500
503 507
504 489
505 502
506 503
507 508
508 504
509 509
510 510
511 511
Sequence Z23, having a sequence length of 256:
[0, 1, 2, 7, 3, 8, 10, 23, 4, 11, 13, 26, 16, 30, 33, 62, 5, 12, 14, 29, 18, 35, 42, 65, 20, 41, 38, 71, 49, 77, 82, 122, 6, 17, 19, 37, 22, 40, 45, 73, 27, 47, 51, 78, 56, 86, 90, 128, 32, 52, 59, 88, 61, 94, 99, 134, 70, 101, 107, 143, 112, 150, 157, 194, 9, 21, 25, 46, 28, 50, 54, 84, 34, 57, 60, 91, 67, 97, 104, 137, 39, 64, 69, 100, 74, 106, 111, 146, 80, 113, 120, 152, 127, 161, 167, 203, 44, 72, 79, 110, 87, 116, 124, 159, 92, 125, 131, 166, 138, 171, 177, 206, 102, 135, 144, 173, 148, 178, 184, 213, 155, 186, 190, 218, 196, 222, 227, 243, 15, 24, 31, 55, 36, 63, 66, 103, 43, 68, 75, 109, 81, 115, 119, 158, 48, 76, 83, 117, 89, 123, 129, 163, 96, 132, 136, 169, 145, 176, 183, 212, 53, 85, 93, 126, 98, 133, 140, 174, 108, 142, 149, 180, 154, 185, 191, 217, 118, 151, 160, 188, 165, 193, 197, 220, 172, 200, 205, 225, 209, 229, 233, 247, 58, 95, 105, 141, 114, 147, 153, 187, 121, 156, 162, 192, 168, 198, 202, 224, 130, 164, 170, 199, 179, 204, 208, 230, 182, 210, 214, 232, 219, 236, 238, 249, 139, 175, 181, 207, 189, 211, 215, 235, 195, 216, 221, 237, 226, 239, 241, 250, 201, 223, 228, 240, 231, 242, 244, 251, 234, 245, 246, 252, 248, 253, 254, 255]
TABLE Z23
having a sequence length of 256:
Polarized channel Reliability or sequence
sequence number number of reliability
0 0
1 1
2 2
3 7
4 3
5 8
6 10
7 23
8 4
9 11
10 13
11 26
12 16
13 30
14 33
15 62
16 5
17 12
18 14
19 29
20 18
21 35
22 42
23 65
24 20
25 41
26 38
27 71
28 49
29 77
30 82
31 122
32 6
33 17
34 19
35 37
36 22
37 40
38 45
39 73
40 27
41 47
42 51
43 78
44 56
45 86
46 90
47 128
48 32
49 52
50 59
51 88
52 61
53 94
54 99
55 134
56 70
57 101
58 107
59 143
60 112
61 150
62 157
63 194
64 9
65 21
66 25
67 46
68 28
69 50
70 54
71 84
72 34
73 57
74 60
75 91
76 67
77 97
78 104
79 137
80 39
81 64
82 69
83 100
84 74
85 106
86 111
87 146
88 80
89 113
90 120
91 152
92 127
93 161
94 167
95 203
96 44
97 72
98 79
99 110
100 87
101 116
102 124
103 159
104 92
105 125
106 131
107 166
108 138
109 171
110 177
111 206
112 102
113 135
114 144
115 173
116 148
117 178
118 184
119 213
120 155
121 186
122 190
123 218
124 196
125 222
126 227
127 243
128 15
129 24
130 31
131 55
132 36
133 63
134 66
135 103
136 43
137 68
138 75
139 109
140 81
141 115
142 119
143 158
144 48
145 76
146 83
147 117
148 89
149 123
150 129
151 163
152 96
153 132
154 136
155 169
156 145
157 176
158 183
159 212
160 53
161 85
162 93
163 126
164 98
165 133
166 140
167 174
168 108
169 142
170 149
171 180
172 154
173 185
174 191
175 217
176 118
177 151
178 160
179 188
180 165
181 193
182 197
183 220
184 172
185 200
186 205
187 225
188 209
189 229
190 233
191 247
192 58
193 95
194 105
195 141
196 114
197 147
198 153
199 187
200 121
201 156
202 162
203 192
204 168
205 198
206 202
207 224
208 130
209 164
210 170
211 199
212 179
213 204
214 208
215 230
216 182
217 210
218 214
219 232
220 219
221 236
222 238
223 249
224 139
225 175
226 181
227 207
228 189
229 211
230 215
231 235
232 195
233 216
234 221
235 237
236 226
237 239
238 241
239 250
240 201
241 223
242 228
243 240
244 231
245 242
246 244
247 251
248 234
249 245
250 246
251 252
252 248
253 253
254 254
255 255
Sequence Z24, having a sequence length of 128:
[0, 1, 2, 7, 3, 8, 10, 22, 4, 11, 13, 24, 15, 28, 30, 53, 5, 12, 14, 27, 17, 32, 38, 55, 19, 37, 34, 59, 43, 63, 67, 90, 6, 16, 18, 33, 21, 36, 40, 61, 25, 42, 45, 64, 48, 69, 72, 94, 29, 46, 50, 71, 52, 75, 77, 96, 58, 79, 83, 100, 86, 104, 107, 119, 9, 20, 23, 41, 26, 44, 47, 68, 31, 49, 51, 73, 56, 76, 81, 98, 35, 54, 57, 78, 62, 82, 85, 102, 66, 87, 89, 105, 93, 109, 111, 121, 39, 60, 65, 84, 70, 88, 91, 108, 74, 92, 95, 110, 99, 112, 114, 122, 80, 97, 101, 113, 103, 115, 116, 123, 106, 117, 118, 124, 120, 125, 126, 127]
TABLE Z24
having a length of 128:
Polarized channel Reliability or sequence
sequence number number of reliability
0 0
1 1
2 2
3 7
4 3
5 8
6 10
7 22
8 4
9 11
10 13
11 24
12 15
13 28
14 30
15 53
16 5
17 12
18 14
19 27
20 17
21 32
22 38
23 55
24 19
25 37
26 34
27 59
28 43
29 63
30 67
31 90
32 6
33 16
34 18
35 33
36 21
37 36
38 40
39 61
40 25
41 42
42 45
43 64
44 48
45 69
46 72
47 94
48 29
49 46
50 50
51 71
52 52
53 75
54 77
55 96
56 58
57 79
58 83
59 100
60 86
61 104
62 107
63 119
64 9
65 20
66 23
67 41
68 26
69 44
70 47
71 68
72 31
73 49
74 51
75 73
76 56
77 76
78 81
79 98
80 35
81 54
82 57
83 78
84 62
85 82
86 85
87 102
88 66
89 87
90 89
91 105
92 93
93 109
94 111
95 121
96 39
97 60
98 65
99 84
100 70
101 88
102 91
103 108
104 74
105 92
106 95
107 110
108 99
109 112
110 114
111 122
112 80
113 97
114 101
115 113
116 103
117 115
118 116
119 123
120 106
121 117
122 118
123 124
124 120
125 125
126 126
127 127
Sequence Z25, having a sequence length of 64:
[0, 1, 2, 7, 3, 8, 9, 20, 4, 10, 12, 21, 14, 24, 26, 41, 5, 11, 13, 23, 16, 27, 32, 42, 18, 31, 29, 44, 35, 46, 48, 57, 6, 15, 17, 28, 19, 30, 33, 45, 22, 34, 36, 47, 38, 49, 51, 58, 25, 37, 39, 50, 40, 52, 53, 59, 43, 54, 55, 60, 56, 61, 62, 63]
TABLE Z25
having a sequence length of 64:
Polarized channel Reliability or sequence
sequence number number of reliability
0 0
1 1
2 2
3 7
4 3
5 8
6 9
7 20
8 4
9 10
10 12
11 21
12 14
13 24
14 26
15 41
16 5
17 11
18 13
19 23
20 16
21 27
22 32
23 42
24 18
25 31
26 29
27 44
28 35
29 46
30 48
31 57
32 6
33 15
34 17
35 28
36 19
37 30
38 33
39 45
40 22
41 34
42 36
43 47
44 38
45 49
46 51
47 58
48 25
49 37
50 39
51 50
52 40
53 52
54 53
55 59
56 43
57 54
58 55
59 60
60 56
61 61
62 62
63 63
Sixth group of sequences (a criterion that considers optimal performance of List 4).
Sequence Q26, having a sequence length of 1024:
[0, 1, 4, 8, 2, 16, 32, 6, 64, 512, 3, 12, 5, 18, 128, 9, 33, 17, 10, 36, 66, 24, 256, 20, 65, 34, 7, 129, 40, 11, 72, 132, 513, 19, 48, 68, 13, 257, 14, 21, 130, 26, 80, 35, 258, 38, 136, 96, 22, 516, 37, 25, 67, 264, 41, 144, 28, 69, 260, 49, 74, 160, 42, 520, 134, 70, 44, 81, 272, 15, 50, 131, 192, 73, 23, 514, 137, 52, 288, 76, 133, 82, 27, 97, 259, 39, 528, 56, 138, 84, 29, 145, 261, 43, 320, 544, 98, 140, 265, 30, 88, 146, 262, 100, 518, 161, 71, 45, 273, 51, 148, 266, 576, 46, 75, 104, 164, 193, 53, 162, 515, 384, 268, 77, 152, 54, 85, 524, 289, 112, 274, 57, 78, 135, 517, 194, 83, 290, 168, 276, 86, 530, 58, 139, 322, 196, 101, 640, 60, 147, 176, 280, 99, 89, 521, 292, 141, 321, 200, 90, 545, 31, 142, 102, 263, 529, 47, 386, 105, 296, 208, 522, 153, 92, 149, 267, 548, 163, 324, 113, 150, 578, 165, 55, 304, 106, 275, 536, 269, 385, 154, 768, 79, 108, 224, 166, 532, 59, 169, 114, 195, 577, 328, 270, 277, 87, 546, 156, 116, 388, 519, 336, 291, 278, 197, 641, 61, 177, 170, 552, 91, 281, 201, 198, 523, 62, 143, 294, 584, 172, 392, 103, 644, 120, 293, 282, 531, 352, 178, 202, 560, 323, 297, 93, 580, 107, 151, 209, 525, 284, 180, 400, 769, 94, 204, 298, 526, 326, 155, 533, 305, 109, 325, 642, 210, 184, 225, 538, 167, 300, 592, 115, 387, 329, 547, 110, 416, 770, 212, 271, 117, 550, 306, 157, 648, 226, 171, 330, 608, 337, 389, 534, 308, 216, 549, 121, 390, 537, 158, 279, 332, 579, 118, 173, 776, 338, 179, 553, 199, 353, 656, 283, 312, 540, 448, 228, 581, 393, 122, 181, 772, 232, 295, 561, 174, 394, 586, 63, 203, 672, 354, 554, 401, 340, 646, 124, 285, 582, 182, 299, 556, 240, 211, 593, 286, 344, 784, 396, 205, 527, 95, 418, 562, 185, 643, 213, 402, 704, 307, 327, 585, 356, 535, 206, 186, 649, 301, 111, 564, 302, 800, 360, 227, 588, 417, 159, 645, 404, 594, 309, 214, 539, 449, 331, 609, 119, 771, 217, 188, 551, 229, 568, 333, 408, 650, 310, 596, 339, 420, 541, 218, 657, 368, 773, 123, 230, 555, 175, 832, 391, 313, 610, 241, 652, 450, 334, 777, 220, 542, 341, 600, 424, 314, 658, 183, 774, 233, 612, 355, 673, 125, 287, 583, 395, 557, 234, 785, 316, 345, 563, 187, 660, 452, 778, 403, 558, 342, 397, 587, 207, 616, 236, 676, 432, 705, 346, 565, 361, 674, 126, 242, 896, 357, 780, 405, 589, 215, 664, 398, 566, 303, 597, 358, 801, 419, 624, 456, 786, 348, 189, 569, 244, 590, 410, 647, 219, 706, 311, 595, 362, 802, 464, 680, 406, 788, 421, 598, 231, 570, 248, 651, 369, 834, 190, 708, 409, 613, 315, 572, 364, 659, 422, 335, 221, 688, 451, 792, 370, 611, 425, 601, 235, 804, 343, 653, 412, 833, 480, 712, 222, 602, 317, 543, 453, 654, 426, 614, 372, 775, 433, 559, 237, 898, 617, 347, 808, 243, 720, 454, 665, 318, 604, 376, 661, 428, 779, 238, 675, 359, 836, 458, 625, 399, 662, 677, 245, 567, 434, 816, 457, 618, 349, 787, 465, 781, 897, 363, 666, 407, 591, 127, 620, 246, 736, 436, 678, 571, 350, 681, 249, 626, 460, 707, 840, 411, 782, 365, 789, 440, 599, 374, 668, 628, 423, 900, 466, 848, 803, 250, 790, 371, 709, 191, 573, 689, 481, 682, 413, 603, 793, 366, 713, 468, 710, 429, 574, 655, 252, 806, 414, 684, 904, 373, 615, 482, 632, 805, 223, 794, 864, 427, 690, 472, 714, 835, 455, 809, 377, 605, 619, 435, 663, 721, 319, 796, 430, 692, 912, 239, 606, 716, 461, 810, 484, 838, 667, 378, 817, 621, 437, 837, 722, 247, 696, 380, 737, 679, 459, 812, 627, 488, 899, 841, 441, 622, 928, 351, 724, 783, 469, 629, 818, 438, 669, 462, 738, 683, 251, 842, 849, 496, 901, 820, 728, 467, 633, 902, 367, 670, 791, 442, 844, 630, 474, 685, 850, 483, 691, 711, 379, 865, 795, 415, 824, 960, 740, 253, 905, 634, 444, 693, 744, 485, 807, 686, 906, 470, 575, 715, 375, 866, 913, 473, 852, 636, 797, 431, 694, 811, 486, 752, 723, 798, 489, 856, 908, 254, 717, 607, 930, 476, 697, 725, 914, 439, 819, 839, 868, 492, 718, 698, 381, 813, 623, 814, 498, 872, 739, 929, 445, 671, 916, 821, 463, 726, 961, 843, 490, 631, 729, 700, 382, 741, 845, 920, 471, 822, 851, 932, 730, 497, 880, 635, 742, 443, 687, 903, 825, 475, 753, 962, 846, 732, 500, 853, 936, 826, 446, 695, 745, 867, 637, 487, 799, 907, 746, 828, 493, 857, 699, 964, 915, 477, 854, 909, 719, 504, 748, 944, 858, 873, 638, 478, 754, 869, 917, 727, 499, 910, 815, 870, 931, 255, 968, 860, 701, 756, 922, 491, 731, 823, 874, 976, 918, 502, 933, 743, 760, 881, 494, 702, 921, 827, 876, 934, 847, 505, 733, 963, 882, 937, 747, 383, 855, 924, 992, 734, 829, 965, 501, 938, 884, 945, 749, 859, 755, 479, 966, 830, 888, 940, 750, 871, 506, 970, 911, 757, 946, 969, 861, 977, 447, 875, 919, 639, 758, 948, 862, 761, 508, 972, 923, 877, 952, 886, 935, 978, 762, 503, 883, 703, 993, 925, 878, 980, 941, 764, 495, 926, 885, 994, 735, 939, 984, 967, 889, 947, 831, 507, 942, 751, 973, 996, 890, 949, 759, 892, 971, 1000, 953, 509, 863, 981, 950, 974, 763, 1008, 979, 879, 954, 986, 995, 891, 927, 510, 765, 956, 997, 982, 887, 985, 943, 998, 1001, 766, 988, 951, 1004, 893, 1010, 957, 975, 511, 1002, 894, 983, 1009, 955, 987, 1012, 958, 999, 1005, 989, 1016, 990, 1011, 767, 1003, 1014, 1006, 1017, 895, 1013, 991, 1018, 959, 1020, 1015, 1007, 1019, 1021, 1022, 1023]
TABLE Q26
having a sequence length of 1024:
Reliability or sequence Polarized channel
number of reliability sequence number
0 0
1 1
2 4
3 8
4 2
5 16
6 32
7 6
8 64
9 512
10 3
11 12
12 5
13 18
14 128
15 9
16 33
17 17
18 10
19 36
20 66
21 24
22 256
23 20
24 65
25 34
26 7
27 129
28 40
29 11
30 72
31 132
32 513
33 19
34 48
35 68
36 13
37 257
38 14
39 21
40 130
41 26
42 80
43 35
44 258
45 38
46 136
47 96
48 22
49 516
50 37
51 25
52 67
53 264
54 41
55 144
56 28
57 69
58 260
59 49
60 74
61 160
62 42
63 520
64 134
65 70
66 44
67 81
68 272
69 15
70 50
71 131
72 192
73 73
74 23
75 514
76 137
77 52
78 288
79 76
80 133
81 82
82 27
83 97
84 259
85 39
86 528
87 56
88 138
89 84
90 29
91 145
92 261
93 43
94 320
95 544
96 98
97 140
98 265
99 30
100 88
101 146
102 262
103 100
104 518
105 161
106 71
107 45
108 273
109 51
110 148
111 266
112 576
113 46
114 75
115 104
116 164
117 193
118 53
119 162
120 515
121 384
122 268
123 77
124 152
125 54
126 85
127 524
128 289
129 112
130 274
131 57
132 78
133 135
134 517
135 194
136 83
137 290
138 168
139 276
140 86
141 530
142 58
143 139
144 322
145 196
146 101
147 640
148 60
149 147
150 176
151 280
152 99
153 89
154 521
155 292
156 141
157 321
158 200
159 90
160 545
161 31
162 142
163 102
164 263
165 529
166 47
167 386
168 105
169 296
170 208
171 522
172 153
173 92
174 149
175 267
176 548
177 163
178 324
179 113
180 150
181 578
182 165
183 55
184 304
185 106
186 275
187 536
188 269
189 385
190 154
191 768
192 79
193 108
194 224
195 166
196 532
197 59
198 169
199 114
200 195
201 577
202 328
203 270
204 277
205 87
206 546
207 156
208 116
209 388
210 519
211 336
212 291
213 278
214 197
215 641
216 61
217 177
218 170
219 552
220 91
221 281
222 201
223 198
224 523
225 62
226 143
227 294
228 584
229 172
230 392
231 103
232 644
233 120
234 293
235 282
236 531
237 352
238 178
239 202
240 560
241 323
242 297
243 93
244 580
245 107
246 151
247 209
248 525
249 284
250 180
251 400
252 769
253 94
254 204
255 298
256 526
257 326
258 155
259 533
260 305
261 109
262 325
263 642
264 210
265 184
266 225
267 538
268 167
269 300
270 592
271 115
272 387
273 329
274 547
275 110
276 416
277 770
278 212
279 271
280 117
281 550
282 306
283 157
284 648
285 226
286 171
287 330
288 608
289 337
290 389
291 534
292 308
293 216
294 549
295 121
296 390
297 537
298 158
299 279
300 332
301 579
302 118
303 173
304 776
305 338
306 179
307 553
308 199
309 353
310 656
311 283
312 312
313 540
314 448
315 228
316 581
317 393
318 122
319 181
320 772
321 232
322 295
323 561
324 174
325 394
326 586
327 63
328 203
329 672
330 354
331 554
332 401
333 340
334 646
335 124
336 285
337 582
338 182
339 299
340 556
341 240
342 211
343 593
344 286
345 344
346 784
347 396
348 205
349 527
350 95
351 418
352 562
353 185
354 643
355 213
356 402
357 704
358 307
359 327
360 585
361 356
362 535
363 206
364 186
365 649
366 301
367 111
368 564
369 302
370 800
371 360
372 227
373 588
374 417
375 159
376 645
377 404
378 594
379 309
380 214
381 539
382 449
383 331
384 609
385 119
386 771
387 217
388 188
389 551
390 229
391 568
392 333
393 408
394 650
395 310
396 596
397 339
398 420
399 541
400 218
401 657
402 368
403 773
404 123
405 230
406 555
407 175
408 832
409 391
410 313
411 610
412 241
413 652
414 450
415 334
416 777
417 220
418 542
419 341
420 600
421 424
422 314
423 658
424 183
425 774
426 233
427 612
428 355
429 673
430 125
431 287
432 583
433 395
434 557
435 234
436 785
437 316
438 345
439 563
440 187
441 660
442 452
443 778
444 403
445 558
446 342
447 397
448 587
449 207
450 616
451 236
452 676
453 432
454 705
455 346
456 565
457 361
458 674
459 126
460 242
461 896
462 357
463 780
464 405
465 589
466 215
467 664
468 398
469 566
470 303
471 597
472 358
473 801
474 419
475 624
476 456
477 786
478 348
479 189
480 569
481 244
482 590
483 410
484 647
485 219
486 706
487 311
488 595
489 362
490 802
491 464
492 680
493 406
494 788
495 421
496 598
497 231
498 570
499 248
500 651
501 369
502 834
503 190
504 708
505 409
506 613
507 315
508 572
509 364
510 659
511 422
512 335
513 221
514 688
515 451
516 792
517 370
518 611
519 425
520 601
521 235
522 804
523 343
524 653
525 412
526 833
527 480
528 712
529 222
530 602
531 317
532 543
533 453
534 654
535 426
536 614
537 372
538 775
539 433
540 559
541 237
542 898
543 617
544 347
545 808
546 243
547 720
548 454
549 665
550 318
551 604
552 376
553 661
554 428
555 779
556 238
557 675
558 359
559 836
560 458
561 625
562 399
563 662
564 677
565 245
566 567
567 434
568 816
569 457
570 618
571 349
572 787
573 465
574 781
575 897
576 363
577 666
578 407
579 591
580 127
581 620
582 246
583 736
584 436
585 678
586 571
587 350
588 681
589 249
590 626
591 460
592 707
593 840
594 411
595 782
596 365
597 789
598 440
599 599
600 374
601 668
602 628
603 423
604 900
605 466
606 848
607 803
608 250
609 790
610 371
611 709
612 191
613 573
614 689
615 481
616 682
617 413
618 603
619 793
620 366
621 713
622 468
623 710
624 429
625 574
626 655
627 252
628 806
629 414
630 684
631 904
632 373
633 615
634 482
635 632
636 805
637 223
638 794
639 864
640 427
641 690
642 472
643 714
644 835
645 455
646 809
647 377
648 605
649 619
650 435
651 663
652 721
653 319
654 796
655 430
656 692
657 912
658 239
659 606
660 716
661 461
662 810
663 484
664 838
665 667
666 378
667 817
668 621
669 437
670 837
671 722
672 247
673 696
674 380
675 737
676 679
677 459
678 812
679 627
680 488
681 899
682 841
683 441
684 622
685 928
686 351
687 724
688 783
689 469
690 629
691 818
692 438
693 669
694 462
695 738
696 683
697 251
698 842
699 849
700 496
701 901
702 820
703 728
704 467
705 633
706 902
707 367
708 670
709 791
710 442
711 844
712 630
713 474
714 685
715 850
716 483
717 691
718 711
719 379
720 865
721 795
722 415
723 824
724 960
725 740
726 253
727 905
728 634
729 444
730 693
731 744
732 485
733 807
734 686
735 906
736 470
737 575
738 715
739 375
740 866
741 913
742 473
743 852
744 636
745 797
746 431
747 694
748 811
749 486
750 752
751 723
752 798
753 489
754 856
755 908
756 254
757 717
758 607
759 930
760 476
761 697
762 725
763 914
764 439
765 819
766 839
767 868
768 492
769 718
770 698
771 381
772 813
773 623
774 814
775 498
776 872
777 739
778 929
779 445
780 671
781 916
782 821
783 463
784 726
785 961
786 843
787 490
788 631
789 729
790 700
791 382
792 741
793 845
794 920
795 471
796 822
797 851
798 932
799 730
800 497
801 880
802 635
803 742
804 443
805 687
806 903
807 825
808 475
809 753
810 962
811 846
812 732
813 500
814 853
815 936
816 826
817 446
818 695
819 745
820 867
821 637
822 487
823 799
824 907
825 746
826 828
827 493
828 857
829 699
830 964
831 915
832 477
833 854
834 909
835 719
836 504
837 748
838 944
839 858
840 873
841 638
842 478
843 754
844 869
845 917
846 727
847 499
848 910
849 815
850 870
851 931
852 255
853 968
854 860
855 701
856 756
857 922
858 491
859 731
860 823
861 874
862 976
863 918
864 502
865 933
866 743
867 760
868 881
869 494
870 702
871 921
872 827
873 876
874 934
875 847
876 505
877 733
878 963
879 882
880 937
881 747
882 383
883 855
884 924
885 992
886 734
887 829
888 965
889 501
890 938
891 884
892 945
893 749
894 859
895 755
896 479
897 966
898 830
899 888
900 940
901 750
902 871
903 506
904 970
905 911
906 757
907 946
908 969
909 861
910 977
911 447
912 875
913 919
914 639
915 758
916 948
917 862
918 761
919 508
920 972
921 923
922 877
923 952
924 886
925 935
926 978
927 762
928 503
929 883
930 703
931 993
932 925
933 878
934 980
935 941
936 764
937 495
938 926
939 885
940 994
941 735
942 939
943 984
944 967
945 889
946 947
947 831
948 507
949 942
950 751
951 973
952 996
953 890
954 949
955 759
956 892
957 971
958 1000
959 953
960 509
961 863
962 981
963 950
964 974
965 763
966 1008
967 979
968 879
969 954
970 986
971 995
972 891
973 927
974 510
975 765
976 956
977 997
978 982
979 887
980 985
981 943
982 998
983 1001
984 766
985 988
986 951
987 1004
988 893
989 1010
990 957
991 975
992 511
993 1002
994 894
995 983
996 1009
997 955
998 987
999 1012
1000 958
1001 999
1002 1005
1003 989
1004 1016
1005 990
1006 1011
1007 767
1008 1003
1009 1014
1010 1006
1011 1017
1012 895
1013 1013
1014 991
1015 1018
1016 959
1017 1020
1018 1015
1019 1007
1020 1019
1021 1021
1022 1022
1023 1023
Sequence Q27, having a sequence length of 512:
[0, 1, 4, 8, 2, 16, 32, 6, 64, 3, 12, 5, 18, 128, 9, 33, 17, 10, 36, 66, 24, 256, 20, 65, 34, 7, 129, 40, 11, 72, 132, 19, 48, 68, 13, 257, 14, 21, 130, 26, 80, 35, 258, 38, 136, 96, 22, 37, 25, 67, 264, 41, 144, 28, 69, 260, 49, 74, 160, 42, 134, 70, 44, 81, 272, 15, 50, 131, 192, 73, 23, 137, 52, 288, 76, 133, 82, 27, 97, 259, 39, 56, 138, 84, 29, 145, 261, 43, 320, 98, 140, 265, 30, 88, 146, 262, 100, 161, 71, 45, 273, 51, 148, 266, 46, 75, 104, 164, 193, 53, 162, 384, 268, 77, 152, 54, 85, 289, 112, 274, 57, 78, 135, 194, 83, 290, 168, 276, 86, 58, 139, 322, 196, 101, 60, 147, 176, 280, 99, 89, 292, 141, 321, 200, 90, 31, 142, 102, 263, 47, 386, 105, 296, 208, 153, 92, 149, 267, 163, 324, 113, 150, 165, 55, 304, 106, 275, 269, 385, 154, 79, 108, 224, 166, 59, 169, 114, 195, 328, 270, 277, 87, 156, 116, 388, 336, 291, 278, 197, 61, 177, 170, 91, 281, 201, 198, 62, 143, 294, 172, 392, 103, 120, 293, 282, 352, 178, 202, 323, 297, 93, 107, 151, 209, 284, 180, 400, 94, 204, 298, 326, 155, 305, 109, 325, 210, 184, 225, 167, 300, 115, 387, 329, 110, 416, 212, 271, 117, 306, 157, 226, 171, 330, 337, 389, 308, 216, 121, 390, 158, 279, 332, 118, 173, 338, 179, 199, 353, 283, 312, 448, 228, 393, 122, 181, 232, 295, 174, 394, 63, 203, 354, 401, 340, 124, 285, 182, 299, 240, 211, 286, 344, 396, 205, 95, 418, 185, 213, 402, 307, 327, 356, 206, 186, 301, 111, 302, 360, 227, 417, 159, 404, 309, 214, 449, 331, 119, 217, 188, 229, 333, 408, 310, 339, 420, 218, 368, 123, 230, 175, 391, 313, 241, 450, 334, 220, 341, 424, 314, 183, 233, 355, 125, 287, 395, 234, 316, 345, 187, 452, 403, 342, 397, 207, 236, 432, 346, 361, 126, 242, 357, 405, 215, 398, 303, 358, 419, 456, 348, 189, 244, 410, 219, 311, 362, 464, 406, 421, 231, 248, 369, 190, 409, 315, 364, 422, 335, 221, 451, 370, 425, 235, 343, 412, 480, 222, 317, 453, 426, 372, 433, 237, 347, 243, 454, 318, 376, 428, 238, 359, 458, 399, 245, 434, 457, 349, 465, 363, 407, 127, 246, 436, 350, 249, 460, 411, 365, 440, 374, 423, 466, 250, 371, 191, 481, 413, 366, 468, 429, 252, 414, 373, 482, 223, 427, 472, 455, 377, 435, 319, 430, 239, 461, 484, 378, 437, 247, 380, 459, 488, 441, 351, 469, 438, 462, 251, 496, 467, 367, 442, 474, 483, 379, 415, 253, 444, 485, 470, 375, 473, 431, 486, 489, 254, 476, 439, 492, 381, 498, 445, 463, 490, 382, 471, 497, 443, 475, 500, 446, 487, 493, 477, 504, 478, 499, 255, 491, 502, 494, 505, 383, 501, 479, 506, 447, 508, 503, 495, 507, 509, 510, 511]
TABLE Q27
having a sequence length of 512:
Reliability or sequence Polarized channel
number of reliability sequence number
0 0
1 1
2 4
3 8
4 2
5 16
6 32
7 6
8 64
9 3
10 12
11 5
12 18
13 128
14 9
15 33
16 17
17 10
18 36
19 66
20 24
21 256
22 20
23 65
24 34
25 7
26 129
27 40
28 11
29 72
30 132
31 19
32 48
33 68
34 13
35 257
36 14
37 21
38 130
39 26
40 80
41 35
42 258
43 38
44 136
45 96
46 22
47 37
48 25
49 67
50 264
51 41
52 144
53 28
54 69
55 260
56 49
57 74
58 160
59 42
60 134
61 70
62 44
63 81
64 272
65 15
66 50
67 131
68 192
69 73
70 23
71 137
72 52
73 288
74 76
75 133
76 82
77 27
78 97
79 259
80 39
81 56
82 138
83 84
84 29
85 145
86 261
87 43
88 320
89 98
90 140
91 265
92 30
93 88
94 146
95 262
96 100
97 161
98 71
99 45
100 273
101 51
102 148
103 266
104 46
105 75
106 104
107 164
108 193
109 53
110 162
111 384
112 268
113 77
114 152
115 54
116 85
117 289
118 112
119 274
120 57
121 78
122 135
123 194
124 83
125 290
126 168
127 276
128 86
129 58
130 139
131 322
132 196
133 101
134 60
135 147
136 176
137 280
138 99
139 89
140 292
141 141
142 321
143 200
144 90
145 31
146 142
147 102
148 263
149 47
150 386
151 105
152 296
153 208
154 153
155 92
156 149
157 267
158 163
159 324
160 113
161 150
162 165
163 55
164 304
165 106
166 275
167 269
168 385
169 154
170 79
171 108
172 224
173 166
174 59
175 169
176 114
177 195
178 328
179 270
180 277
181 87
182 156
183 116
184 388
185 336
186 291
187 278
188 197
189 61
190 177
191 170
192 91
193 281
194 201
195 198
196 62
197 143
198 294
199 172
200 392
201 103
202 120
203 293
204 282
205 352
206 178
207 202
208 323
209 297
210 93
211 107
212 151
213 209
214 284
215 180
216 400
217 94
218 204
219 298
220 326
221 155
222 305
223 109
224 325
225 210
226 184
227 225
228 167
229 300
230 115
231 387
232 329
233 110
234 416
235 212
236 271
237 117
238 306
239 157
240 226
241 171
242 330
243 337
244 389
245 308
246 216
247 121
248 390
249 158
250 279
251 332
252 118
253 173
254 338
255 179
256 199
257 353
258 283
259 312
260 448
261 228
262 393
263 122
264 181
265 232
266 295
267 174
268 394
269 63
270 203
271 354
272 401
273 340
274 124
275 285
276 182
277 299
278 240
279 211
280 286
281 344
282 396
283 205
284 95
285 418
286 185
287 213
288 402
289 307
290 327
291 356
292 206
293 186
294 301
295 111
296 302
297 360
298 227
299 417
300 159
301 404
302 309
303 214
304 449
305 331
306 119
307 217
308 188
309 229
310 333
311 408
312 310
313 339
314 420
315 218
316 368
317 123
318 230
319 175
320 391
321 313
322 241
323 450
324 334
325 220
326 341
327 424
328 314
329 183
330 233
331 355
332 125
333 287
334 395
335 234
336 316
337 345
338 187
339 452
340 403
341 342
342 397
343 207
344 236
345 432
346 346
347 361
348 126
349 242
350 357
351 405
352 215
353 398
354 303
355 358
356 419
357 456
358 348
359 189
360 244
361 410
362 219
363 311
364 362
365 464
366 406
367 421
368 231
369 248
370 369
371 190
372 409
373 315
374 364
375 422
376 335
377 221
378 451
379 370
380 425
381 235
382 343
383 412
384 480
385 222
386 317
387 453
388 426
389 372
390 433
391 237
392 347
393 243
394 454
395 318
396 376
397 428
398 238
399 359
400 458
401 399
402 245
403 434
404 457
405 349
406 465
407 363
408 407
409 127
410 246
411 436
412 350
413 249
414 460
415 411
416 365
417 440
418 374
419 423
420 466
421 250
422 371
423 191
424 481
425 413
426 366
427 468
428 429
429 252
430 414
431 373
432 482
433 223
434 427
435 472
436 455
437 377
438 435
439 319
440 430
441 239
442 461
443 484
444 378
445 437
446 247
447 380
448 459
449 488
450 441
451 351
452 469
453 438
454 462
455 251
456 496
457 467
458 367
459 442
460 474
461 483
462 379
463 415
464 253
465 444
466 485
467 470
468 375
469 473
470 431
471 486
472 489
473 254
474 476
475 439
476 492
477 381
478 498
479 445
480 463
481 490
482 382
483 471
484 497
485 443
486 475
487 500
488 446
489 487
490 493
491 477
492 504
493 478
494 499
495 255
496 491
497 502
498 494
499 505
500 383
501 501
502 479
503 506
504 447
505 508
506 503
507 495
508 507
509 509
510 510
511 511
Sequence Q28, having a sequence length of 256:
[0, 1, 4, 8, 2, 16, 32, 6, 64, 3, 12, 5, 18, 128, 9, 33, 17, 10, 36, 66, 24, 20, 65, 34, 7, 129, 40, 11, 72, 132, 19, 48, 68, 13, 14, 21, 130, 26, 80, 35, 38, 136, 96, 22, 37, 25, 67, 41, 144, 28, 69, 49, 74, 160, 42, 134, 70, 44, 81, 15, 50, 131, 192, 73, 23, 137, 52, 76, 133, 82, 27, 97, 39, 56, 138, 84, 29, 145, 43, 98, 140, 30, 88, 146, 100, 161, 71, 45, 51, 148, 46, 75, 104, 164, 193, 53, 162, 77, 152, 54, 85, 112, 57, 78, 135, 194, 83, 168, 86, 58, 139, 196, 101, 60, 147, 176, 99, 89, 141, 200, 90, 31, 142, 102, 47, 105, 208, 153, 92, 149, 163, 113, 150, 165, 55, 106, 154, 79, 108, 224, 166, 59, 169, 114, 195, 87, 156, 116, 197, 61, 177, 170, 91, 201, 198, 62, 143, 172, 103, 120, 178, 202, 93, 107, 151, 209, 180, 94, 204, 155, 109, 210, 184, 225, 167, 115, 110, 212, 117, 157, 226, 171, 216, 121, 158, 118, 173, 179, 199, 228, 122, 181, 232, 174, 63, 203, 124, 182, 240, 211, 205, 95, 185, 213, 206, 186, 111, 227, 159, 214, 119, 217, 188, 229, 218, 123, 230, 175, 241, 220, 183, 233, 125, 234, 187, 207, 236, 126, 242, 215, 189, 244, 219, 231, 248, 190, 221, 235, 222, 237, 243, 238, 245, 127, 246, 249, 250, 191, 252, 223, 239, 247, 251, 253, 254, 255]
TABLE Q28
having a sequence length of 256:
Reliability or sequence Polarized channel
number of reliability sequence number
0 0
1 1
2 4
3 8
4 2
5 16
6 32
7 6
8 64
9 3
10 12
11 5
12 18
13 128
14 9
15 33
16 17
17 10
18 36
19 66
20 24
21 20
22 65
23 34
24 7
25 129
26 40
27 11
28 72
29 132
30 19
31 48
32 68
33 13
34 14
35 21
36 130
37 26
38 80
39 35
40 38
41 136
42 96
43 22
44 37
45 25
46 67
47 41
48 144
49 28
50 69
51 49
52 74
53 160
54 42
55 134
56 70
57 44
58 81
59 15
60 50
61 131
62 192
63 73
64 23
65 137
66 52
67 76
68 133
69 82
70 27
71 97
72 39
73 56
74 138
75 84
76 29
77 145
78 43
79 98
80 140
81 30
82 88
83 146
84 100
85 161
86 71
87 45
88 51
89 148
90 46
91 75
92 104
93 164
94 193
95 53
96 162
97 77
98 152
99 54
100 85
101 112
102 57
103 78
104 135
105 194
106 83
107 168
108 86
109 58
110 139
111 196
112 101
113 60
114 147
115 176
116 99
117 89
118 141
119 200
120 90
121 31
122 142
123 102
124 47
125 105
126 208
127 153
128 92
129 149
130 163
131 113
132 150
133 165
134 55
135 106
136 154
137 79
138 108
139 224
140 166
141 59
142 169
143 114
144 195
145 87
146 156
147 116
148 197
149 61
150 177
151 170
152 91
153 201
154 198
155 62
156 143
157 172
158 103
159 120
160 178
161 202
162 93
163 107
164 151
165 209
166 180
167 94
168 204
169 155
170 109
171 210
172 184
173 225
174 167
175 115
176 110
177 212
178 117
179 157
180 226
181 171
182 216
183 121
184 158
185 118
186 173
187 179
188 199
189 228
190 122
191 181
192 232
193 174
194 63
195 203
196 124
197 182
198 240
199 211
200 205
201 95
202 185
203 213
204 206
205 186
206 111
207 227
208 159
209 214
210 119
211 217
212 188
213 229
214 218
215 123
216 230
217 175
218 241
219 220
220 183
221 233
222 125
223 234
224 187
225 207
226 236
227 126
228 242
229 215
230 189
231 244
232 219
233 231
234 248
235 190
236 221
237 235
238 222
239 237
240 243
241 238
242 245
243 127
244 246
245 249
246 250
247 191
248 252
249 223
250 239
251 247
252 251
253 253
254 254
255 255
Sequence Q29, having a sequence length of 128:
[0, 1, 4, 8, 2, 16, 32, 6, 64, 3, 12, 5, 18, 9, 33, 17, 10, 36, 66, 24, 20, 65, 34, 7, 40, 11, 72, 19, 48, 68, 13, 14, 21, 26, 80, 35, 38, 96, 22, 37, 25, 67, 41, 28, 69, 49, 74, 42, 70, 44, 81, 15, 50, 73, 23, 52, 76, 82, 27, 97, 39, 56, 84, 29, 43, 98, 30, 88, 100, 71, 45, 51, 46, 75, 104, 53, 77, 54, 85, 112, 57, 78, 83, 86, 58, 101, 60, 99, 89, 90, 31, 102, 47, 105, 92, 113, 55, 106, 79, 108, 59, 114, 87, 116, 61, 91, 62, 103, 120, 93, 107, 94, 109, 115, 110, 117, 121, 118, 122, 63, 124, 95, 111, 119, 123, 125, 126, 127]
TABLE Q29
having a sequence length of 128:
Reliability or sequence Polarized channel
number of reliability sequence number
0 0
1 1
2 4
3 8
4 2
5 16
6 32
7 6
8 64
9 3
10 12
11 5
12 18
13 9
14 33
15 17
16 10
17 36
18 66
19 24
20 20
21 65
22 34
23 7
24 40
25 11
26 72
27 19
28 48
29 68
30 13
31 14
32 21
33 26
34 80
35 35
36 38
37 96
38 22
39 37
40 25
41 67
42 41
43 28
44 69
45 49
46 74
47 42
48 70
49 44
50 81
51 15
52 50
53 73
54 23
55 52
56 76
57 82
58 27
59 97
60 39
61 56
62 84
63 29
64 43
65 98
66 30
67 88
68 100
69 71
70 45
71 51
72 46
73 75
74 104
75 53
76 77
77 54
78 85
79 112
80 57
81 78
82 83
83 86
84 58
85 101
86 60
87 99
88 89
89 90
90 31
91 102
92 47
93 105
94 92
95 113
96 55
97 106
98 79
99 108
100 59
101 114
102 87
103 116
104 61
105 91
106 62
107 103
108 120
109 93
110 107
111 94
112 109
113 115
114 110
115 117
116 121
117 118
118 122
119 63
120 124
121 95
122 111
123 119
124 123
125 125
126 126
127 127
Sequence Q30, having a sequence length of 64:
[0, 1, 4, 8, 2, 16, 32, 6, 3, 12, 5, 18, 9, 33, 17, 10, 36, 24, 20, 34, 7, 40, 11, 19, 48, 13, 14, 21, 26, 35, 38, 22, 37, 25, 41, 28, 49, 42, 44, 15, 50, 23, 52, 27, 39, 56, 29, 43, 30, 45, 51, 46, 53, 54, 57, 58, 60, 31, 47, 55, 59, 61, 62, 63]
TABLE Q30
having a sequence length of 64:
Reliability Polarized
or sequence channel
number of sequence
reliability number
0 0
1 1
2 4
3 8
4 2
5 16
6 32
7 6
8 3
9 12
10 5
11 18
12 9
13 33
14 17
15 10
16 36
17 24
18 20
19 34
20 7
21 40
22 11
23 19
24 48
25 13
26 14
27 21
28 26
29 35
30 38
31 22
32 37
33 25
34 41
35 28
36 49
37 42
38 44
39 15
40 50
41 23
42 52
43 27
44 39
45 56
46 29
47 43
48 30
49 45
50 51
51 46
52 53
53 54
54 57
55 58
56 60
57 31
58 47
59 55
60 59
61 61
62 62
63 63
Sequence Z26, having a sequence length of 1024:
[0, 1, 4, 10, 2, 12, 7, 26, 3, 15, 18, 29, 11, 36, 38, 69, 5, 17, 13, 33, 23, 39, 48, 74, 21, 51, 41, 82, 56, 90, 99, 161, 6, 16, 25, 43, 19, 50, 45, 85, 28, 54, 62, 93, 66, 107, 113, 166, 34, 59, 70, 109, 77, 118, 125, 183, 87, 131, 142, 197, 148, 216, 225, 327, 8, 24, 20, 52, 35, 57, 65, 106, 30, 73, 60, 114, 79, 123, 132, 192, 42, 67, 81, 136, 89, 126, 140, 205, 100, 153, 159, 220, 173, 243, 253, 350, 47, 83, 96, 152, 103, 146, 163, 231, 115, 168, 185, 245, 193, 261, 275, 367, 129, 179, 199, 271, 208, 280, 302, 385, 233, 295, 318, 404, 335, 430, 459, 580, 14, 27, 40, 71, 31, 80, 64, 133, 46, 76, 88, 143, 97, 156, 162, 226, 55, 91, 101, 149, 110, 174, 180, 246, 124, 172, 190, 258, 207, 283, 298, 375, 61, 105, 119, 177, 116, 182, 195, 268, 138, 198, 218, 286, 229, 303, 324, 407, 150, 217, 238, 306, 250, 319, 338, 424, 265, 353, 364, 440, 388, 479, 503, 612, 72, 117, 135, 200, 145, 214, 223, 308, 158, 222, 239, 328, 254, 348, 363, 449, 170, 247, 264, 342, 278, 355, 380, 466, 293, 387, 400, 485, 417, 513, 529, 637, 194, 266, 285, 372, 315, 390, 405, 497, 321, 426, 435, 521, 451, 541, 556, 658, 341, 412, 460, 546, 481, 565, 582, 672, 499, 589, 608, 697, 627, 726, 756, 852, 22, 37, 44, 84, 58, 92, 102, 164, 53, 98, 111, 175, 122, 188, 203, 279, 68, 108, 130, 186, 139, 204, 213, 299, 151, 221, 235, 311, 249, 336, 344, 431, 78, 128, 137, 212, 155, 234, 227, 322, 169, 242, 255, 339, 269, 366, 369, 470, 184, 260, 282, 358, 292, 379, 395, 487, 312, 410, 422, 507, 437, 531, 550, 653, 94, 157, 144, 241, 178, 262, 257, 359, 202, 273, 287, 383, 300, 392, 415, 512, 211, 289, 305, 397, 333, 419, 446, 523, 345, 438, 455, 544, 478, 571, 587, 686, 237, 309, 330, 428, 361, 462, 472, 558, 371, 457, 489, 576, 509, 596, 620, 707, 402, 501, 517, 610, 537, 632, 600, 739, 552, 647, 666, 719, 674, 771, 791, 882, 121, 189, 167, 272, 209, 290, 296, 409, 230, 317, 325, 433, 347, 447, 468, 562, 251, 332, 356, 444, 377, 464, 493, 578, 393, 505, 483, 594, 525, 617, 629, 722, 276, 374, 351, 474, 398, 495, 511, 603, 421, 519, 535, 640, 554, 624, 655, 746, 453, 539, 567, 650, 584, 669, 692, 764, 598, 683, 710, 804, 729, 779, 817, 911, 314, 382, 414, 515, 442, 533, 548, 645, 476, 569, 560, 677, 591, 661, 694, 783, 491, 573, 605, 704, 622, 689, 736, 795, 642, 742, 713, 808, 760, 832, 842, 896, 527, 615, 634, 716, 663, 732, 749, 822, 680, 753, 787, 858, 768, 827, 869, 937, 700, 800, 775, 847, 813, 889, 864, 928, 836, 876, 903, 948, 919, 960, 974, 992, 9, 32, 75, 120, 49, 134, 104, 210, 63, 154, 171, 224, 127, 248, 256, 349, 86, 165, 141, 236, 196, 259, 291, 362, 187, 297, 267, 381, 313, 399, 418, 532, 95, 160, 206, 274, 176, 294, 281, 389, 219, 307, 331, 406, 340, 434, 445, 540, 240, 323, 352, 439, 368, 456, 469, 566, 391, 480, 498, 586, 508, 613, 625, 737, 112, 201, 181, 301, 244, 316, 337, 432, 228, 360, 326, 448, 373, 465, 482, 579, 270, 343, 378, 488, 396, 471, 496, 599, 420, 520, 530, 618, 551, 648, 659, 758, 288, 384, 411, 518, 427, 506, 536, 633, 450, 543, 570, 649, 581, 668, 684, 773, 475, 561, 590, 679, 602, 690, 712, 788, 635, 705, 728, 802, 744, 821, 841, 914, 147, 215, 263, 354, 232, 376, 334, 484, 284, 365, 394, 500, 413, 524, 534, 626, 310, 401, 423, 510, 441, 553, 563, 651, 467, 549, 577, 665, 601, 693, 708, 780, 329, 429, 458, 557, 452, 564, 585, 676, 492, 588, 616, 696, 630, 714, 734, 805, 514, 614, 641, 717, 656, 730, 747, 818, 673, 761, 770, 829, 790, 855, 870, 930, 357, 454, 486, 592, 504, 611, 623, 718, 528, 621, 643, 738, 660, 757, 769, 835, 547, 652, 671, 751, 687, 762, 784, 846, 703, 789, 799, 859, 812, 877, 886, 941, 583, 675, 695, 777, 725, 792, 803, 866, 731, 819, 825, 881, 837, 893, 901, 950, 750, 809, 843, 895, 856, 906, 915, 955, 867, 918, 927, 965, 936, 975, 984, 1007, 191, 252, 277, 386, 320, 403, 425, 538, 304, 416, 443, 555, 463, 574, 595, 688, 346, 436, 477, 572, 494, 597, 609, 709, 516, 619, 638, 721, 654, 745, 752, 823, 370, 473, 490, 607, 522, 636, 628, 733, 545, 646, 662, 748, 678, 772, 774, 849, 568, 667, 691, 765, 702, 782, 796, 860, 723, 807, 816, 872, 826, 887, 898, 947, 408, 526, 502, 644, 559, 670, 664, 766, 593, 682, 698, 786, 711, 793, 811, 875, 606, 699, 715, 797, 743, 814, 833, 883, 754, 828, 839, 894, 854, 909, 917, 961, 639, 720, 740, 820, 767, 844, 850, 902, 776, 840, 861, 912, 873, 922, 933, 968, 801, 868, 879, 929, 891, 939, 924, 979, 899, 945, 953, 972, 956, 988, 994, 1012, 461, 575, 542, 681, 604, 701, 706, 806, 631, 727, 735, 824, 755, 834, 848, 905, 657, 741, 763, 831, 781, 845, 863, 913, 794, 871, 857, 921, 884, 932, 938, 973, 685, 778, 759, 851, 798, 865, 874, 925, 815, 880, 890, 942, 900, 935, 949, 981, 838, 892, 907, 946, 916, 954, 963, 986, 923, 959, 969, 997, 976, 990, 1000, 1016, 724, 785, 810, 878, 830, 888, 897, 944, 853, 908, 904, 957, 920, 951, 964, 991, 862, 910, 926, 967, 934, 962, 978, 995, 943, 980, 970, 998, 985, 1003, 1005, 1014, 885, 931, 940, 971, 952, 977, 982, 1001, 958, 983, 993, 1008, 987, 1002, 1010, 1019, 966, 996, 989, 1006, 999, 1013, 1009, 1018, 1004, 1011, 1015, 1020, 1017, 1021, 1022, 1023]
TABLE Z26
having a sequence length of 1024:
Polarized channel Reliability or sequence
sequence number number of reliability
0 0
1 1
2 4
3 10
4 2
5 12
6 7
7 26
8 3
9 15
10 18
11 29
12 11
13 36
14 38
15 69
16 5
17 17
18 13
19 33
20 23
21 39
22 48
23 74
24 21
25 51
26 41
27 82
28 56
29 90
30 99
31 161
32 6
33 16
34 25
35 43
36 19
37 50
38 45
39 85
40 28
41 54
42 62
43 93
44 66
45 107
46 113
47 166
48 34
49 59
50 70
51 109
52 77
53 118
54 125
55 183
56 87
57 131
58 142
59 197
60 148
61 216
62 225
63 327
64 8
65 24
66 20
67 52
68 35
69 57
70 65
71 106
72 30
73 73
74 60
75 114
76 79
77 123
78 132
79 192
80 42
81 67
82 81
83 136
84 89
85 126
86 140
87 205
88 100
89 153
90 159
91 220
92 173
93 243
94 253
95 350
96 47
97 83
98 96
99 152
100 103
101 146
102 163
103 231
104 115
105 168
106 185
107 245
108 193
109 261
110 275
111 367
112 129
113 179
114 199
115 271
116 208
117 280
118 302
119 385
120 233
121 295
122 318
123 404
124 335
125 430
126 459
127 580
128 14
129 27
130 40
131 71
132 31
133 80
134 64
135 133
136 46
137 76
138 88
139 143
140 97
141 156
142 162
143 226
144 55
145 91
146 101
147 149
148 110
149 174
150 180
151 246
152 124
153 172
154 190
155 258
156 207
157 283
158 298
159 375
160 61
161 105
162 119
163 177
164 116
165 182
166 195
167 268
168 138
169 198
170 218
171 286
172 229
173 303
174 324
175 407
176 150
177 217
178 238
179 306
180 250
181 319
182 338
183 424
184 265
185 353
186 364
187 440
188 388
189 479
190 503
191 612
192 72
193 117
194 135
195 200
196 145
197 214
198 223
199 308
200 158
201 222
202 239
203 328
204 254
205 348
206 363
207 449
208 170
209 247
210 264
211 342
212 278
213 355
214 380
215 466
216 293
217 387
218 400
219 485
220 417
221 513
222 529
223 637
224 194
225 266
226 285
227 372
228 315
229 390
230 405
231 497
232 321
233 426
234 435
235 521
236 451
237 541
238 556
239 658
240 341
241 412
242 460
243 546
244 481
245 565
246 582
247 672
248 499
249 589
250 608
251 697
252 627
253 726
254 756
255 852
256 22
257 37
258 44
259 84
260 58
261 92
262 102
263 164
264 53
265 98
266 111
267 175
268 122
269 188
270 203
271 279
272 68
273 108
274 130
275 186
276 139
277 204
278 213
279 299
280 151
281 221
282 235
283 311
284 249
285 336
286 344
287 431
288 78
289 128
290 137
291 212
292 155
293 234
294 227
295 322
296 169
297 242
298 255
299 339
300 269
301 366
302 369
303 470
304 184
305 260
306 282
307 358
308 292
309 379
310 395
311 487
312 312
313 410
314 422
315 507
316 437
317 531
318 550
319 653
320 94
321 157
322 144
323 241
324 178
325 262
326 257
327 359
328 202
329 273
330 287
331 383
332 300
333 392
334 415
335 512
336 211
337 289
338 305
339 397
340 333
341 419
342 446
343 523
344 345
345 438
346 455
347 544
348 478
349 571
350 587
351 686
352 237
353 309
354 330
355 428
356 361
357 462
358 472
359 558
360 371
361 457
362 489
363 576
364 509
365 596
366 620
367 707
368 402
369 501
370 517
371 610
372 537
373 632
374 600
375 739
376 552
377 647
378 666
379 719
380 674
381 771
382 791
383 882
384 121
385 189
386 167
387 272
388 209
389 290
390 296
391 409
392 230
393 317
394 325
395 433
396 347
397 447
398 468
399 562
400 251
401 332
402 356
403 444
404 377
405 464
406 493
407 578
408 393
409 505
410 483
411 594
412 525
413 617
414 629
415 722
416 276
417 374
418 351
419 474
420 398
421 495
422 511
423 603
424 421
425 519
426 535
427 640
428 554
429 624
430 655
431 746
432 453
433 539
434 567
435 650
436 584
437 669
438 692
439 764
440 598
441 683
442 710
443 804
444 729
445 779
446 817
447 911
448 314
449 382
450 414
451 515
452 442
453 533
454 548
455 645
456 476
457 569
458 560
459 677
460 591
461 661
462 694
463 783
464 491
465 573
466 605
467 704
468 622
469 689
470 736
471 795
472 642
473 742
474 713
475 808
476 760
477 832
478 842
479 896
480 527
481 615
482 634
483 716
484 663
485 732
486 749
487 822
488 680
489 753
490 787
491 858
492 768
493 827
494 869
495 937
496 700
497 800
498 775
499 847
500 813
501 889
502 864
503 928
504 836
505 876
506 903
507 948
508 919
509 960
510 974
511 992
512 9
513 32
514 75
515 120
516 49
517 134
518 104
519 210
520 63
521 154
522 171
523 224
524 127
525 248
526 256
527 349
528 86
529 165
530 141
531 236
532 196
533 259
534 291
535 362
536 187
537 297
538 267
539 381
540 313
541 399
542 418
543 532
544 95
545 160
546 206
547 274
548 176
549 294
550 281
551 389
552 219
553 307
554 331
555 406
556 340
557 434
558 445
559 540
560 240
561 323
562 352
563 439
564 368
565 456
566 469
567 566
568 391
569 480
570 498
571 586
572 508
573 613
574 625
575 737
576 112
577 201
578 181
579 301
580 244
581 316
582 337
583 432
584 228
585 360
586 326
587 448
588 373
589 465
590 482
591 579
592 270
593 343
594 378
595 488
596 396
597 471
598 496
599 599
600 420
601 520
602 530
603 618
604 551
605 648
606 659
607 758
608 288
609 384
610 411
611 518
612 427
613 506
614 536
615 633
616 450
617 543
618 570
619 649
620 581
621 668
622 684
623 773
624 475
625 561
626 590
627 679
628 602
629 690
630 712
631 788
632 635
633 705
634 728
635 802
636 744
637 821
638 841
639 914
640 147
641 215
642 263
643 354
644 232
645 376
646 334
647 484
648 284
649 365
650 394
651 500
652 413
653 524
654 534
655 626
656 310
657 401
658 423
659 510
660 441
661 553
662 563
663 651
664 467
665 549
666 577
667 665
668 601
669 693
670 708
671 780
672 329
673 429
674 458
675 557
676 452
677 564
678 585
679 676
680 492
681 588
682 616
683 696
684 630
685 714
686 734
687 805
688 514
689 614
690 641
691 717
692 656
693 730
694 747
695 818
696 673
697 761
698 770
699 829
700 790
701 855
702 870
703 930
704 357
705 454
706 486
707 592
708 504
709 611
710 623
711 718
712 528
713 621
714 643
715 738
716 660
717 757
718 769
719 835
720 547
721 652
722 671
723 751
724 687
725 762
726 784
727 846
728 703
729 789
730 799
731 859
732 812
733 877
734 886
735 941
736 583
737 675
738 695
739 777
740 725
741 792
742 803
743 866
744 731
745 819
746 825
747 881
748 837
749 893
750 901
751 950
752 750
753 809
754 843
755 895
756 856
757 906
758 915
759 955
760 867
761 918
762 927
763 965
764 936
765 975
766 984
767 1007
768 191
769 252
770 277
771 386
772 320
773 403
774 425
775 538
776 304
777 416
778 443
779 555
780 463
781 574
782 595
783 688
784 346
785 436
786 477
787 572
788 494
789 597
790 609
791 709
792 516
793 619
794 638
795 721
796 654
797 745
798 752
799 823
800 370
801 473
802 490
803 607
804 522
805 636
806 628
807 733
808 545
809 646
810 662
811 748
812 678
813 772
814 774
815 849
816 568
817 667
818 691
819 765
820 702
821 782
822 796
823 860
824 723
825 807
826 816
827 872
828 826
829 887
830 898
831 947
832 408
833 526
834 502
835 644
836 559
837 670
838 664
839 766
840 593
841 682
842 698
843 786
844 711
845 793
846 811
847 875
848 606
849 699
850 715
851 797
852 743
853 814
854 833
855 883
856 754
857 828
858 839
859 894
860 854
861 909
862 917
863 961
864 639
865 720
866 740
867 820
868 767
869 844
870 850
871 902
872 776
873 840
874 861
875 912
876 873
877 922
878 933
879 968
880 801
881 868
882 879
883 929
884 891
885 939
886 924
887 979
888 899
889 945
890 953
891 972
892 956
893 988
894 994
895 1012
896 461
897 575
898 542
899 681
900 604
901 701
902 706
903 806
904 631
905 727
906 735
907 824
908 755
909 834
910 848
911 905
912 657
913 741
914 763
915 831
916 781
917 845
918 863
919 913
920 794
921 871
922 857
923 921
924 884
925 932
926 938
927 973
928 685
929 778
930 759
931 851
932 798
933 865
934 874
935 925
936 815
937 880
938 890
939 942
940 900
941 935
942 949
943 981
944 838
945 892
946 907
947 946
948 916
949 954
950 963
951 986
952 923
953 959
954 969
955 997
956 976
957 990
958 1000
959 1016
960 724
961 785
962 810
963 878
964 830
965 888
966 897
967 944
968 853
969 908
970 904
971 957
972 920
973 951
974 964
975 991
976 862
977 910
978 926
979 967
980 934
981 962
982 978
983 995
984 943
985 980
986 970
987 998
988 985
989 1003
990 1005
991 1014
992 885
993 931
994 940
995 971
996 952
997 977
998 982
999 1001
1000 958
1001 983
1002 993
1003 1008
1004 987
1005 1002
1006 1010
1007 1019
1008 966
1009 996
1010 989
1011 1006
1012 999
1013 1013
1014 1009
1015 1018
1016 1004
1017 1011
1018 1015
1019 1020
1020 1017
1021 1021
1022 1022
1023 1023
Sequence Z27, having a sequence length of 512:
[0, 1, 4, 9, 2, 11, 7, 25, 3, 14, 17, 28, 10, 34, 36, 65, 5, 16, 12, 31, 22, 37, 46, 70, 20, 48, 39, 77, 53, 84, 92, 145, 6, 15, 24, 41, 18, 47, 43, 80, 27, 51, 59, 87, 62, 99, 104, 149, 32, 56, 66, 101, 72, 109, 115, 163, 81, 120, 129, 174, 134, 189, 196, 269, 8, 23, 19, 49, 33, 54, 61, 98, 29, 69, 57, 105, 74, 113, 121, 170, 40, 63, 76, 124, 83, 116, 128, 181, 93, 139, 144, 192, 155, 210, 217, 284, 45, 78, 89, 138, 96, 133, 147, 201, 106, 151, 165, 211, 171, 223, 233, 295, 118, 160, 176, 230, 183, 237, 252, 306, 202, 247, 263, 317, 274, 332, 348, 409, 13, 26, 38, 67, 30, 75, 60, 122, 44, 71, 82, 130, 90, 141, 146, 197, 52, 85, 94, 135, 102, 156, 161, 212, 114, 154, 169, 221, 182, 239, 249, 300, 58, 97, 110, 158, 107, 162, 173, 228, 126, 175, 191, 241, 199, 253, 267, 319, 136, 190, 206, 255, 215, 264, 276, 329, 226, 286, 293, 338, 308, 359, 371, 423, 68, 108, 123, 177, 132, 188, 195, 256, 143, 194, 207, 270, 218, 283, 292, 343, 153, 213, 225, 279, 235, 287, 303, 352, 246, 307, 315, 362, 325, 377, 385, 433, 172, 227, 240, 298, 261, 309, 318, 368, 265, 330, 335, 381, 344, 391, 398, 441, 278, 322, 349, 393, 360, 402, 410, 446, 369, 413, 421, 455, 429, 464, 473, 495, 21, 35, 42, 79, 55, 86, 95, 148, 50, 91, 103, 157, 112, 167, 179, 236, 64, 100, 119, 166, 127, 180, 187, 250, 137, 193, 204, 258, 214, 275, 280, 333, 73, 117, 125, 186, 140, 203, 198, 266, 152, 209, 219, 277, 229, 294, 296, 354, 164, 222, 238, 289, 245, 302, 312, 363, 259, 321, 328, 373, 336, 386, 395, 439, 88, 142, 131, 208, 159, 224, 220, 290, 178, 232, 242, 305, 251, 310, 324, 376, 185, 243, 254, 313, 273, 326, 341, 382, 281, 337, 346, 392, 358, 405, 412, 451, 205, 257, 271, 331, 291, 350, 355, 399, 297, 347, 364, 407, 374, 416, 426, 458, 316, 370, 379, 422, 389, 431, 418, 468, 396, 437, 444, 462, 447, 477, 482, 500, 111, 168, 150, 231, 184, 244, 248, 320, 200, 262, 268, 334, 282, 342, 353, 401, 216, 272, 288, 340, 301, 351, 366, 408, 311, 372, 361, 415, 383, 425, 430, 463, 234, 299, 285, 356, 314, 367, 375, 419, 327, 380, 388, 434, 397, 428, 440, 470, 345, 390, 403, 438, 411, 445, 453, 475, 417, 450, 459, 485, 465, 479, 488, 504, 260, 304, 323, 378, 339, 387, 394, 436, 357, 404, 400, 448, 414, 442, 454, 480, 365, 406, 420, 457, 427, 452, 467, 483, 435, 469, 460, 486, 474, 491, 493, 502, 384, 424, 432, 461, 443, 466, 471, 489, 449, 472, 481, 496, 476, 490, 498, 507, 456, 484, 478, 494, 487, 501, 497, 506, 492, 499, 503, 508, 505, 509, 510, 511]
TABLE Z27
having a sequence length of 512:
Polarized channel Reliability or sequence
sequence number number of reliability
0 0
1 1
2 4
3 9
4 2
5 11
6 7
7 25
8 3
9 14
10 17
11 28
12 10
13 34
14 36
15 65
16 5
17 16
18 12
19 31
20 22
21 37
22 46
23 70
24 20
25 48
26 39
27 77
28 53
29 84
30 92
31 145
32 6
33 15
34 24
35 41
36 18
37 47
38 43
39 80
40 27
41 51
42 59
43 87
44 62
45 99
46 104
47 149
48 32
49 56
50 66
51 101
52 72
53 109
54 115
55 163
56 81
57 120
58 129
59 174
60 134
61 189
62 196
63 269
64 8
65 23
66 19
67 49
68 33
69 54
70 61
71 98
72 29
73 69
74 57
75 105
76 74
77 113
78 121
79 170
80 40
81 63
82 76
83 124
84 83
85 116
86 128
87 181
88 93
89 139
90 144
91 192
92 155
93 210
94 217
95 284
96 45
97 78
98 89
99 138
100 96
101 133
102 147
103 201
104 106
105 151
106 165
107 211
108 171
109 223
110 233
111 295
112 118
113 160
114 176
115 230
116 183
117 237
118 252
119 306
120 202
121 247
122 263
123 317
124 274
125 332
126 348
127 409
128 13
129 26
130 38
131 67
132 30
133 75
134 60
135 122
136 44
137 71
138 82
139 130
140 90
141 141
142 146
143 197
144 52
145 85
146 94
147 135
148 102
149 156
150 161
151 212
152 114
153 154
154 169
155 221
156 182
157 239
158 249
159 300
160 58
161 97
162 110
163 158
164 107
165 162
166 173
167 228
168 126
169 175
170 191
171 241
172 199
173 253
174 267
175 319
176 136
177 190
178 206
179 255
180 215
181 264
182 276
183 329
184 226
185 286
186 293
187 338
188 308
189 359
190 371
191 423
192 68
193 108
194 123
195 177
196 132
197 188
198 195
199 256
200 143
201 194
202 207
203 270
204 218
205 283
206 292
207 343
208 153
209 213
210 225
211 279
212 235
213 287
214 303
215 352
216 246
217 307
218 315
219 362
220 325
221 377
222 385
223 433
224 172
225 227
226 240
227 298
228 261
229 309
230 318
231 368
232 265
233 330
234 335
235 381
236 344
237 391
238 398
239 441
240 278
241 322
242 349
243 393
244 360
245 402
246 410
247 446
248 369
249 413
250 421
251 455
252 429
253 464
254 473
255 495
256 21
257 35
258 42
259 79
260 55
261 86
262 95
263 148
264 50
265 91
266 103
267 157
268 112
269 167
270 179
271 236
272 64
273 100
274 119
275 166
276 127
277 180
278 187
279 250
280 137
281 193
282 204
283 258
284 214
285 275
286 280
287 333
288 73
289 117
290 125
291 186
292 140
293 203
294 198
295 266
296 152
297 209
298 219
299 277
300 229
301 294
302 296
303 354
304 164
305 222
306 238
307 289
308 245
309 302
310 312
311 363
312 259
313 321
314 328
315 373
316 336
317 386
318 395
319 439
320 88
321 142
322 131
323 208
324 159
325 224
326 220
327 290
328 178
329 232
330 242
331 305
332 251
333 310
334 324
335 376
336 185
337 243
338 254
339 313
340 273
341 326
342 341
343 382
344 281
345 337
346 346
347 392
348 358
349 405
350 412
351 451
352 205
353 257
354 271
355 331
356 291
357 350
358 355
359 399
360 297
361 347
362 364
363 407
364 374
365 416
366 426
367 458
368 316
369 370
370 379
371 422
372 389
373 431
374 418
375 468
376 396
377 437
378 444
379 462
380 447
381 477
382 482
383 500
384 111
385 168
386 150
387 231
388 184
389 244
390 248
391 320
392 200
393 262
394 268
395 334
396 282
397 342
398 353
399 401
400 216
401 272
402 288
403 340
404 301
405 351
406 366
407 408
408 311
409 372
410 361
411 415
412 383
413 425
414 430
415 463
416 234
417 299
418 285
419 356
420 314
421 367
422 375
423 419
424 327
425 380
426 388
427 434
428 397
429 428
430 440
431 470
432 345
433 390
434 403
435 438
436 411
437 445
438 453
439 475
440 417
441 450
442 459
443 485
444 465
445 479
446 488
447 504
448 260
449 304
450 323
451 378
452 339
453 387
454 394
455 436
456 357
457 404
458 400
459 448
460 414
461 442
462 454
463 480
464 365
465 406
466 420
467 457
468 427
469 452
470 467
471 483
472 435
473 469
474 460
475 486
476 474
477 491
478 493
479 502
480 384
481 424
482 432
483 461
484 443
485 466
486 471
487 489
488 449
489 472
490 481
491 496
492 476
493 490
494 498
495 507
496 456
497 484
498 478
499 494
500 487
501 501
502 497
503 506
504 492
505 499
506 503
507 508
508 505
509 509
510 510
511 511
Sequence Z28, having a sequence length of 256:
[0, 1, 4, 9, 2, 11, 7, 24, 3, 14, 17, 27, 10, 33, 34, 59, 5, 16, 12, 30, 21, 35, 43, 64, 20, 45, 37, 70, 49, 76, 81, 121, 6, 15, 23, 39, 18, 44, 40, 72, 26, 47, 54, 78, 57, 87, 90, 124, 31, 51, 60, 88, 66, 95, 99, 134, 73, 102, 109, 141, 113, 149, 155, 194, 8, 22, 19, 46, 32, 50, 56, 86, 28, 63, 52, 91, 67, 97, 103, 137, 38, 58, 69, 106, 75, 100, 108, 145, 82, 117, 120, 152, 128, 162, 167, 201, 42, 71, 79, 116, 84, 112, 123, 158, 92, 125, 135, 163, 138, 170, 176, 206, 101, 131, 143, 175, 147, 178, 185, 210, 159, 183, 190, 215, 196, 222, 227, 243, 13, 25, 36, 61, 29, 68, 55, 104, 41, 65, 74, 110, 80, 118, 122, 156, 48, 77, 83, 114, 89, 129, 132, 164, 98, 127, 136, 169, 146, 179, 184, 208, 53, 85, 96, 130, 93, 133, 140, 174, 107, 142, 151, 181, 157, 186, 193, 217, 115, 150, 160, 187, 166, 191, 197, 220, 172, 202, 205, 224, 212, 230, 235, 247, 62, 94, 105, 144, 111, 148, 154, 188, 119, 153, 161, 195, 168, 200, 204, 225, 126, 165, 171, 199, 177, 203, 209, 229, 182, 211, 214, 232, 219, 236, 238, 249, 139, 173, 180, 207, 189, 213, 216, 233, 192, 221, 223, 237, 226, 239, 241, 250, 198, 218, 228, 240, 231, 242, 244, 251, 234, 245, 246, 252, 248, 253, 254, 255]
TABLE Z28
having a sequence length of 256:
Polarized channel Reliability or sequence
sequence number number of reliability
0 0
1 1
2 4
3 9
4 2
5 11
6 7
7 24
8 3
9 14
10 17
11 27
12 10
13 33
14 34
15 59
16 5
17 16
18 12
19 30
20 21
21 35
22 43
23 64
24 20
25 45
26 37
27 70
28 49
29 76
30 81
31 121
32 6
33 15
34 23
35 39
36 18
37 44
38 40
39 72
40 26
41 47
42 54
43 78
44 57
45 87
46 90
47 124
48 31
49 51
50 60
51 88
52 66
53 95
54 99
55 134
56 73
57 102
58 109
59 141
60 113
61 149
62 155
63 194
64 8
65 22
66 19
67 46
68 32
69 50
70 56
71 86
72 28
73 63
74 52
75 91
76 67
77 97
78 103
79 137
80 38
81 58
82 69
83 106
84 75
85 100
86 108
87 145
88 82
89 117
90 120
91 152
92 128
93 162
94 167
95 201
96 42
97 71
98 79
99 116
100 84
101 112
102 123
103 158
104 92
105 125
106 135
107 163
108 138
109 170
110 176
111 206
112 101
113 131
114 143
115 175
116 147
117 178
118 185
119 210
120 159
121 183
122 190
123 215
124 196
125 222
126 227
127 243
128 13
129 25
130 36
131 61
132 29
133 68
134 55
135 104
136 41
137 65
138 74
139 110
140 80
141 118
142 122
143 156
144 48
145 77
146 83
147 114
148 89
149 129
150 132
151 164
152 98
153 127
154 136
155 169
156 146
157 179
158 184
159 208
160 53
161 85
162 96
163 130
164 93
165 133
166 140
167 174
168 107
169 142
170 151
171 181
172 157
173 186
174 193
175 217
176 115
177 150
178 160
179 187
180 166
181 191
182 197
183 220
184 172
185 202
186 205
187 224
188 212
189 230
190 235
191 247
192 62
193 94
194 105
195 144
196 111
197 148
198 154
199 188
200 119
201 153
202 161
203 195
204 168
205 200
206 204
207 225
208 126
209 165
210 171
211 199
212 177
213 203
214 209
215 229
216 182
217 211
218 214
219 232
220 219
221 236
222 238
223 249
224 139
225 173
226 180
227 207
228 189
229 213
230 216
231 233
232 192
233 221
234 223
235 237
236 226
237 239
238 241
239 250
240 198
241 218
242 228
243 240
244 231
245 242
246 244
247 251
248 234
249 245
250 246
251 252
252 248
253 253
254 254
255 255
Sequence Z29, having a sequence length of 128:
[0, 1, 4, 9, 2, 11, 7, 23, 3, 13, 16, 25, 10, 30, 31, 51, 5, 15, 12, 27, 20, 32, 38, 54, 19, 40, 33, 58, 43, 63, 66, 90, 6, 14, 22, 35, 17, 39, 36, 60, 24, 42, 47, 64, 49, 70, 72, 92, 28, 45, 52, 71, 55, 75, 77, 96, 61, 80, 84, 100, 86, 104, 106, 119, 8, 21, 18, 41, 29, 44, 48, 69, 26, 53, 46, 73, 56, 76, 81, 98, 34, 50, 57, 82, 62, 78, 83, 102, 67, 88, 89, 105, 94, 109, 111, 121, 37, 59, 65, 87, 68, 85, 91, 107, 74, 93, 97, 110, 99, 112, 114, 122, 79, 95, 101, 113, 103, 115, 117, 123, 108, 116, 118, 124, 120, 125, 126, 127]
TABLE Z29
having a sequence length of 128:
Polarized channel Reliability or sequence
sequence number number of reliability
0 0
1 1
2 4
3 9
4 2
5 11
6 7
7 23
8 3
9 13
10 16
11 25
12 10
13 30
14 31
15 51
16 5
17 15
18 12
19 27
20 20
21 32
22 38
23 54
24 19
25 40
26 33
27 58
28 43
29 63
30 66
31 90
32 6
33 14
34 22
35 35
36 17
37 39
38 36
39 60
40 24
41 42
42 47
43 64
44 49
45 70
46 72
47 92
48 28
49 45
50 52
51 71
52 55
53 75
54 77
55 96
56 61
57 80
58 84
59 100
60 86
61 104
62 106
63 119
64 8
65 21
66 18
67 41
68 29
69 44
70 48
71 69
72 26
73 53
74 46
75 73
76 56
77 76
78 81
79 98
80 34
81 50
82 57
83 82
84 62
85 78
86 83
87 102
88 67
89 88
90 89
91 105
92 94
93 109
94 111
95 121
96 37
97 59
98 65
99 87
100 68
101 85
102 91
103 107
104 74
105 93
106 97
107 110
108 99
109 112
110 114
111 122
112 79
113 95
114 101
115 113
116 103
117 115
118 117
119 123
120 108
121 116
122 118
123 124
124 120
125 125
126 126
127 127
Sequence Z30, having a sequence length of 64:
[0, 1, 4, 8, 2, 10, 7, 20, 3, 12, 15, 22, 9, 25, 26, 39, 5, 14, 11, 23, 18, 27, 31, 41, 17, 33, 28, 43, 35, 46, 48, 57, 6, 13, 19, 29, 16, 32, 30, 44, 21, 34, 37, 47, 38, 49, 51, 58, 24, 36, 40, 50, 42, 52, 53, 59, 45, 54, 55, 60, 56, 61, 62, 63]
TABLE Z30
having a sequence length of 64:
Polarized channel Reliability or sequence
sequence number number of reliability
0 0
1 1
2 4
3 8
4 2
5 10
6 7
7 20
8 3
9 12
10 15
11 22
12 9
13 25
14 26
15 39
16 5
17 14
18 11
19 23
20 18
21 27
22 31
23 41
24 17
25 33
26 28
27 43
28 35
29 46
30 48
31 57
32 6
33 13
34 19
35 29
36 16
37 32
38 30
39 44
40 21
41 34
42 37
43 47
44 38
45 49
46 51
47 58
48 24
49 36
50 40
51 50
52 42
53 52
54 53
55 59
56 45
57 54
58 55
59 60
60 56
61 61
62 62
63 63
It should be noted that, the foregoing sequences are merely some examples. Use of the foregoing sequences in a polar code encoding process helps improve encoding/decoding performance of a polar code. In any one of the sequences described, adjustments or equivalent replacements in the following aspects may be made without affecting an overall effect.
1. Positions of a small quantity of elements in a sequence are interchanged. For example, a position of a sequence number may be adjusted within a specified range. For example, the specified range is 5, and a position of an element whose sequence number is 10 may be adjusted within five positions to the left or right.
2. Some of the elements in the sequence are adjusted, but channel sets for transmitting T bit information that are selected based on the sequence are consistent or similar.
3. The sequence includes N elements starting from 0 and ending with N−1, and the N elements starting from 0 and ending with N−1 represent sequence numbers of N polarized channels. Actually, the sequence numbers of the N polarized channels may also start from 1 and end with N. This can be achieved by adding 1 to each sequence number in the foregoing sequence, and this is also a sequence number form in the foregoing calculation manners. Certainly, the sequence number or an identifier of the foregoing polarized channel may also be represented by using another manner. The specific representation manner does not affect a specific position of a polarized channel in a sequence;
4. The sequence numbers of the N polarized channels in the foregoing sequence are arranged in ascending order of the reliability of the N polarized channels. In this case, selecting K polarized channels in descending order of reliability is selecting polarized channels that correspond to the last K sequence numbers in any of the foregoing sequences. Actually, the sequence numbers of the N polarized channels may also be arranged in descending order of the reliability of the N polarized channels. This can be achieved by arranging the elements in the foregoing sequence in a reverse or inverted order. In this case, selecting K polarized channels in descending order of reliability is selecting polarized channels that correspond to the first K sequence numbers; and
5. The foregoing sequences may further be represented by using a normalized reliability or an equivalent reliability of each channel. For example, if a sequential position of a channel x in the foregoing sequence is n (a leftmost position is denoted as 1), a reliability of the channel may be represented as n or normalized n/N, where N is a length of the sequence.
Based on a same invention concept of the polar code encoding method shown in FIG. 2, as shown in FIG. 3, an embodiment of this application further provides a polar code encoding apparatus 300. The polar code encoding apparatus 300 is configured to perform the polar code encoding method shown in FIG. 2. Part or all of the polar code encoding method shown in FIG. 3 may be implemented by using hardware or may be implemented by using software. When part or all of the polar code encoding method is implemented by using hardware, the polar code encoding apparatus 300 includes: an input interface circuit 301, configured to obtain to-be-encoded bits; a logic circuit 302, configured to perform the polar code encoding method shown in FIG. 2, where for details, refer to the descriptions in the foregoing method embodiments, and details are not described herein again; and an output interface circuit 303, configured to output a bit sequence after encoding.
Further, the bit sequence that is obtained after the encoding and that is output by the encoding apparatus 300 is output to a transceiver 320 after being modulated by a modulator 310. The transceiver 320 performs corresponding processing (including but not limited to processing such as digital-to-analog conversion and/or frequency conversion) on the modulated sequence and sends the processed sequence by using an antenna 330.
Optionally, the polar code encoding apparatus 300 may be a chip or an integrated circuit during specific implementation.
Optionally, when part or all of the polar code encoding method in the foregoing embodiment is implemented by using software, as shown in FIG. 4, the polar code encoding apparatus 300 includes: a memory 401, configured to store a program; a processor 402, configured to execute the program stored in the memory 401. When the program is executed, the polar code encoding apparatus 300 is caused to implement the polar code encoding method provided in the embodiment in FIG. 2.
Optionally, the memory 401 may be a physically independent unit. Alternatively, as shown in FIG. 5, a memory 501 is integrated with a processor 502.
Optionally, when part of or all of the encoding method in the embodiment in FIG. 2 is implemented by using software, the polar code encoding apparatus 300 may include only the processor 402. The memory 401 configured to store the program is located outside the polar code encoding apparatus 300. The processor 402 is connected to the memory 401 by using a circuit/wire and is configured to read and execute the program stored in the memory 401.
The processor 402 may be a central processing unit (CPU), a network processor (NP), or a combination of a CPU and an NP.
The processor 402 may further include a hardware chip. The foregoing hardware chip may be an application-specific integrated circuit (ASIC), a programmable logic device (PLD), or a combination of an ASIC and a PLD. The foregoing PLD may be a complex programmable logical device (CPLD), a field-programmable gate array (FPGA), a generic array logic (GAL), or any combination thereof.
The memory in the foregoing embodiment may include a volatile memory, for example, a random-access memory (RAM). Alternatively, the memory may include a non-volatile memory, for example, a flash memory, a hard disk drive (HDD), or a solid-state drive (SSD). Alternatively, the memory may include a combination of the foregoing types of memories.
Based on the polar code encoding method shown in FIG. 2, as shown in FIG. 6, an embodiment of this application further provides a polar code encoding apparatus 300. The polar code encoding apparatus 300 is configured to perform the polar code encoding method shown in FIG. 2. The polar code encoding apparatus 300 includes:
an obtaining unit 601, configured to obtain a first sequence used to encode K to-be-encoded bits, where the first sequence includes sequence numbers of N polarized channels, the sequence numbers of the N polarized channels are arranged in the first sequence based on reliability of the N polarized channels, K is a positive integer, N is a mother code length of a polar code, N is a positive integer power of 2, and K≤N;
a selection unit 602, configured to select sequence numbers of K polarized channels from the first sequence in ascending order of the reliability; and
an encoding unit 603, configured to place the to-be-encoded bits based on the selected sequence numbers of the K polarized channels, and perform polar code encoding on the to-be-encoded bits.
The first sequence may be any one of the sequences described above, or may be a sequence obtained by selecting, from a second sequence having a length of Nmax, sequence numbers (starting from 0) less than N. The second sequence may be any one of the sequences described above. A reliability of an ith polarized channel in the N polarized channels may be determined by using any one of the formulas described above.
An embodiment of this application further provides a computer storage medium storing a computer program. The computer program is configured to perform the polar code encoding method shown in FIG. 2.
An embodiment of this application further provides a computer program product including an instruction. When run on a computer, the instruction causes the computer to perform the polar code encoding method shown in FIG. 2.
Persons skilled in the art should understand that the embodiments of this application may be provided as a method, a system, or a computer program product. Therefore, this application may use a form of hardware only embodiments, software only embodiments, or embodiments with a combination of software and hardware. Moreover, this application may use a form of a computer program product that is implemented on one or more computer-usable storage media (including but not limited to a disk memory, a CD-ROM, an optical memory, and the like) that include computer usable program code.
This application is described with reference to the flowcharts and/or block diagrams of the method, the device (system), and the computer program product according to the embodiments of this application. It should be understood that computer program instructions may be used to implement each process and/or each block in the flowcharts and/or the block diagrams and a combination of a process and/or a block in the flowcharts and/or the block diagrams. These computer program instructions may be provided for a general-purpose computer, a dedicated computer, an embedded processor, or a processor of any other programmable data processing device to generate a machine, so that the instructions executed by a computer or a processor of any other programmable data processing device generate an apparatus for implementing a specific function in one or more processes in the flowcharts and/or in one or more blocks in the block diagrams.
These computer program instructions may be stored in a computer readable memory that can instruct the computer or any other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory generate an artifact that includes an instruction apparatus. The instruction apparatus implements a specific function in one or more processes in the flowcharts and/or in one or more blocks in the block diagrams.
These computer program instructions may be loaded onto a computer or another programmable data processing device, so that a series of operations and steps are performed on the computer or the another programmable device, thereby generating computer-implemented processing. Therefore, the instructions executed on the computer or the another programmable device provide steps for implementing a specific function in one or more processes in the flowcharts and/or in one or more blocks in the block diagrams.
Although some preferred embodiments of this application have been described, persons skilled in the art can make changes and modifications to these embodiments once they learn the basic inventive concept. Therefore, the following claims are intended to be construed as to cover the preferred embodiments and all changes and modifications falling within the scope of this application.
Obviously, persons skilled in the art can make various modifications and variations to the embodiments of this application without departing from the spirit and scope of the embodiments of this application. This application is intended to cover these modifications and variations provided that they fall within the scope of protection defined by the following claims and their equivalent technologies.

Claims (24)

What is claimed is:
1. An encoding method, comprising:
obtaining, by an encoding apparatus, a first sequence used to encode K to-be-encoded bits, the first sequence comprising sequence numbers of N polarized channels, wherein the first sequence is same as a second sequence or a subset of the second sequence, the second sequence comprises sequence numbers of Nmax polarized channels, K is a positive integer, N=2n, n is a positive integer, n is equal to or greater than 5, K≤N, and Nmax=1024;
selecting, by the encoding apparatus, sequence numbers of K polarized channels from the first sequence;
performing, by the encoding apparatus, polar code encoding on the K to-be-encoded bits based on the selected sequence numbers of the K polarized channels, to obtain a bit sequence after encoding; and
outputting, by the encoding apparatus, the bit sequence after encoding to a receiving device;
wherein the second sequence is the sequence shown in Sequence Q11 or Table Q11;
the Sequence Q11 comprising:
[0, 1, 2, 4, 8, 16, 32, 3, 5, 64, 9, 6, 17, 10, 18, 128, 12, 33, 65, 20, 256, 34, 24, 36, 7, 129, 66, 512, 11, 40, 68, 130, 19, 13, 48, 14, 72, 257, 21, 132, 35, 258, 26, 513, 80, 37, 25, 22, 136, 260, 264, 38, 514, 96, 67, 41, 144, 28, 69, 42, 516, 49, 74, 272, 160, 520, 288, 528, 192, 544, 70, 44, 131, 81, 50, 73, 15, 320, 133, 52, 23, 134, 384, 76, 137, 82, 56, 27, 97, 39, 259, 84, 138, 145, 261, 29, 43, 98, 515, 88, 140, 30, 146, 71, 262, 265, 161, 576, 45, 100, 640, 51, 148, 46, 75, 266, 273, 517, 104, 162, 53, 193, 152, 77, 164, 768, 268, 274, 518, 54, 83, 57, 521, 112, 135, 78, 289, 194, 85, 276, 522, 58, 168, 139, 99, 86, 60, 280, 89, 290, 529, 524, 196, 141, 101, 147, 176, 142, 530, 321, 31, 200, 90, 545, 292, 322, 532, 263, 149, 102, 105, 304, 296, 163, 92, 47, 267, 385, 546, 324, 208, 386, 150, 153, 165, 106, 55, 328, 536, 577, 548, 113, 154, 79, 269, 108, 578, 224, 166, 519, 552, 195, 270, 641, 523, 275, 580, 291, 59, 169, 560, 114, 277, 156, 87, 197, 116, 170, 61, 531, 525, 642, 281, 278, 526, 177, 293, 388, 91, 584, 769, 198, 172, 120, 201, 336, 62, 282, 143, 103, 178, 294, 93, 644, 202, 592, 323, 392, 297, 770, 107, 180, 151, 209, 284, 648, 94, 204, 298, 400, 608, 352, 325, 533, 155, 210, 305, 547, 300, 109, 184, 534, 537, 115, 167, 225, 326, 306, 772, 157, 656, 329, 110, 117, 212, 171, 776, 330, 226, 549, 538, 387, 308, 216, 416, 271, 279, 158, 337, 550, 672, 118, 332, 579, 540, 389, 173, 121, 553, 199, 784, 179, 228, 338, 312, 704, 390, 174, 554, 581, 393, 283, 122, 448, 353, 561, 203, 63, 340, 394, 527, 582, 556, 181, 295, 285, 232, 124, 205, 182, 643, 562, 286, 585, 299, 354, 211, 401, 185, 396, 344, 586, 645, 593, 535, 240, 206, 95, 327, 564, 800, 402, 356, 307, 301, 417, 213, 568, 832, 588, 186, 646, 404, 227, 896, 594, 418, 302, 649, 771, 360, 539, 111, 331, 214, 309, 188, 449, 217, 408, 609, 596, 551, 650, 229, 159, 420, 310, 541, 773, 610, 657, 333, 119, 600, 339, 218, 368, 652, 230, 391, 313, 450, 542, 334, 233, 555, 774, 175, 123, 658, 612, 341, 777, 220, 314, 424, 395, 673, 583, 355, 287, 183, 234, 125, 557, 660, 616, 342, 316, 241, 778, 563, 345, 452, 397, 403, 207, 674, 558, 785, 432, 357, 187, 236, 664, 624, 587, 780, 705, 126, 242, 565, 398, 346, 456, 358, 405, 303, 569, 244, 595, 189, 566, 676, 361, 706, 589, 215, 786, 647, 348, 419, 406, 464, 680, 801, 362, 590, 409, 570, 788, 597, 572, 219, 311, 708, 598, 601, 651, 421, 792, 802, 611, 602, 410, 231, 688, 653, 248, 369, 190, 364, 654, 659, 335, 480, 315, 221, 370, 613, 422, 425, 451, 614, 543, 235, 412, 343, 372, 775, 317, 222, 426, 453, 237, 559, 833, 804, 712, 834, 661, 808, 779, 617, 604, 433, 720, 816, 836, 347, 897, 243, 662, 454, 318, 675, 618, 898, 781, 376, 428, 665, 736, 567, 840, 625, 238, 359, 457, 399, 787, 591, 678, 434, 677, 349, 245, 458, 666, 620, 363, 127, 191, 782, 407, 436, 626, 571, 465, 681, 246, 707, 350, 599, 668, 790, 460, 249, 682, 573, 411, 803, 789, 709, 365, 440, 628, 689, 374, 423, 466, 793, 250, 371, 481, 574, 413, 603, 366, 468, 655, 900, 805, 615, 684, 710, 429, 794, 252, 373, 605, 848, 690, 713, 632, 482, 806, 427, 904, 414, 223, 663, 692, 835, 619, 472, 455, 796, 809, 714, 721, 837, 716, 864, 810, 606, 912, 722, 696, 377, 435, 817, 319, 621, 812, 484, 430, 838, 667, 488, 239, 378, 459, 622, 627, 437, 380, 818, 461, 496, 669, 679, 724, 841, 629, 351, 467, 438, 737, 251, 462, 442, 441, 469, 247, 683, 842, 738, 899, 670, 783, 849, 820, 728, 928, 791, 367, 901, 630, 685, 844, 633, 711, 253, 691, 824, 902, 686, 740, 850, 375, 444, 470, 483, 415, 485, 905, 795, 473, 634, 744, 852, 960, 865, 693, 797, 906, 715, 807, 474, 636, 694, 254, 717, 575, 913, 798, 811, 379, 697, 431, 607, 489, 866, 723, 486, 908, 718, 813, 476, 856, 839, 725, 698, 914, 752, 868, 819, 814, 439, 929, 490, 623, 671, 739, 916, 463, 843, 381, 497, 930, 821, 726, 961, 872, 492, 631, 729, 700, 443, 741, 845, 920, 382, 822, 851, 730, 498, 880, 742, 445, 471, 635, 932, 687, 903, 825, 500, 846, 745, 826, 732, 446, 962, 936, 475, 853, 867, 637, 907, 487, 695, 746, 828, 753, 854, 857, 504, 799, 255, 964, 909, 719, 477, 915, 638, 748, 944, 869, 491, 699, 754, 858, 478, 968, 383, 910, 815, 976, 870, 917, 727, 493, 873, 701, 931, 756, 860, 499, 731, 823, 922, 874, 918, 502, 933, 743, 760, 881, 494, 702, 921, 501, 876, 847, 992, 447, 733, 827, 934, 882, 937, 963, 747, 505, 855, 924, 734, 829, 965, 938, 884, 506, 749, 945, 966, 755, 859, 940, 830, 911, 871, 639, 888, 479, 946, 750, 969, 508, 861, 757, 970, 919, 875, 862, 758, 948, 977, 923, 972, 761, 877, 952, 495, 703, 935, 978, 883, 762, 503, 925, 878, 735, 993, 885, 939, 994, 980, 926, 764, 941, 967, 886, 831, 947, 507, 889, 984, 751, 942, 996, 971, 890, 509, 949, 973, 1000, 892, 950, 863, 759, 1008, 510, 979, 953, 763, 974, 954, 879, 981, 982, 927, 995, 765, 956, 887, 985, 997, 986, 943, 891, 998, 766, 511, 988, 1001, 951, 1002, 893, 975, 894, 1009, 955, 1004, 1010, 957, 983, 958, 987, 1012, 999, 1016, 767, 989, 1003, 990, 1005, 959, 1011, 1013, 895, 1006, 1014, 1017, 1018, 991, 1020, 1007, 1015, 1019, 1021, 1022, 1023];
the Table Q11 comprising:
Reliability or sequence Polarized channel number of reliability sequence number 0 0 1 1 2 2 3 4 4 8 5 16 6 32 7 3 8 5 9 64 10 9 11 6 12 17 13 10 14 18 15 128 16 12 17 33 18 65 19 20 20 256 21 34 22 24 23 36 24 7 25 129 26 66 27 512 28 11 29 40 30 68 31 130 32 19 33 13 34 48 35 14 36 72 37 257 38 21 39 132 40 35 41 258 42 26 43 513 44 80 45 37 46 25 47 22 48 136 49 260 50 264 51 38 52 514 53 96 54 67 55 41 56 144 57 28 58 69 59 42 60 516 61 49 62 74 63 272 64 160 65 520 66 288 67 528 68 192 69 544 70 70 71 44 72 131 73 81 74 50 75 73 76 15 77 320 78 133 79 52 80 23 81 134 82 384 83 76 84 137 85 82 86 56 87 27 88 97 89 39 90 259 91 84 92 138 93 145 94 261 95 29 96 43 97 98 98 515 99 88 100 140 101 30 102 146 103 71 104 262 105 265 106 161 107 576 108 45 109 100 110 640 111 51 112 148 113 46 114 75 115 266 116 273 117 517 118 104 119 162 120 53 121 193 122 152 123 77 124 164 125 768 126 268 127 274 128 518 129 54 130 83 131 57 132 521 133 112 134 135 135 78 136 289 137 194 138 85 139 276 140 522 141 58 142 168 143 139 144 99 145 86 146 60 147 280 148 89 149 290 150 529 151 524 152 196 153 141 154 101 155 147 156 176 157 142 158 530 159 321 160 31 161 200 162 90 163 545 164 292 165 322 166 532 167 263 168 149 169 102 170 105 171 304 172 296 173 163 174 92 175 47 176 267 177 385 178 546 179 324 180 208 181 386 182 150 183 153 184 165 185 106 186 55 187 328 188 536 189 577 190 548 191 113 192 154 193 79 194 269 195 108 196 578 197 224 198 166 199 519 200 552 201 195 202 270 203 641 204 523 205 275 206 580 207 291 208 59 209 169 210 560 211 114 212 277 213 156 214 87 215 197 216 116 217 170 218 61 219 531 220 525 221 642 222 281 223 278 224 526 225 177 226 293 227 388 228 91 229 584 230 769 231 198 232 172 233 120 234 201 235 336 236 62 237 282 238 143 239 103 240 178 241 294 242 93 243 644 244 202 245 592 246 323 247 392 248 297 249 770 250 107 251 180 252 151 253 209 254 284 255 648 256 94 257 204 258 298 259 400 260 608 261 352 262 325 263 533 264 155 265 210 266 305 267 547 268 300 269 109 270 184 271 534 272 537 273 115 274 167 275 225 276 326 277 306 278 772 279 157 280 656 281 329 282 110 283 117 284 212 285 171 286 776 287 330 288 226 289 549 290 538 291 387 292 308 293 216 294 416 295 271 296 279 297 158 298 337 299 550 300 672 301 118 302 332 303 579 304 540 305 389 306 173 307 121 308 553 309 199 310 784 311 179 312 228 313 338 314 312 315 704 316 390 317 174 318 554 319 581 320 393 321 283 322 122 323 448 324 353 325 561 326 203 327 63 328 340 329 394 330 527 331 582 332 556 333 181 334 295 335 285 336 232 337 124 338 205 339 182 340 643 341 562 342 286 343 585 344 299 345 354 346 211 347 401 348 185 349 396 350 344 351 586 352 645 353 593 354 535 355 240 356 206 357 95 358 327 359 564 360 800 361 402 362 356 363 307 364 301 365 417 366 213 367 568 368 832 369 588 370 186 371 646 372 404 373 227 374 896 375 594 376 418 377 302 378 649 379 771 380 360 381 539 382 111 383 331 384 214 385 309 386 188 387 449 388 217 389 408 390 609 391 596 392 551 393 650 394 229 395 159 396 420 397 310 398 541 399 773 400 610 401 657 402 333 403 119 404 600 405 339 406 218 407 368 408 652 409 230 410 391 411 313 412 450 413 542 414 334 415 233 416 555 417 774 418 175 419 123 420 658 421 612 422 341 423 777 424 220 425 314 426 424 427 395 428 673 429 583 430 355 431 287 432 183 433 234 434 125 435 557 436 660 437 616 438 342 439 316 440 241 441 778 442 563 443 345 444 452 445 397 446 403 447 207 448 674 449 558 450 785 451 432 452 357 453 187 454 236 455 664 456 624 457 587 458 780 459 705 460 126 461 242 462 565 463 398 464 346 465 456 466 358 467 405 468 303 469 569 470 244 471 595 472 189 473 566 474 676 475 361 476 706 477 589 478 215 479 786 480 647 481 348 482 419 483 406 484 464 485 680 486 801 487 362 488 590 489 409 490 570 491 788 492 597 493 572 494 219 495 311 496 708 497 598 498 601 499 651 500 421 501 792 502 802 503 611 504 602 505 410 506 231 507 688 508 653 509 248 510 369 511 190 512 364 513 654 514 659 515 335 516 480 517 315 518 221 519 370 520 613 521 422 522 425 523 451 524 614 525 543 526 235 527 412 528 343 529 372 530 775 531 317 532 222 533 426 534 453 535 237 536 559 537 833 538 804 539 712 540 834 541 661 542 808 543 779 544 617 545 604 546 433 547 720 548 816 549 836 550 347 551 897 552 243 553 662 554 454 555 318 556 675 557 618 558 898 559 781 560 376 561 428 562 665 563 736 564 567 565 840 566 625 567 238 568 359 569 457 570 399 571 787 572 591 573 678 574 434 575 677 576 349 577 245 578 458 579 666 580 620 581 363 582 127 583 191 584 782 585 407 586 436 587 626 588 571 589 465 590 681 591 246 592 707 593 350 594 599 595 668 596 790 597 460 598 249 599 682 600 573 601 411 602 803 603 789 604 709 605 365 606 440 607 628 608 689 609 374 610 423 611 466 612 793 613 250 614 371 615 481 616 574 617 413 618 603 619 366 620 468 621 655 622 900 623 805 624 615 625 684 626 710 627 429 628 794 629 252 630 373 631 605 632 848 633 690 634 713 635 632 636 482 637 806 638 427 639 904 640 414 641 223 642 663 643 692 644 835 645 619 646 472 647 455 648 796 649 809 650 714 651 721 652 837 653 716 654 864 655 810 656 606 657 912 658 722 659 696 660 377 661 435 662 817 663 319 664 621 665 812 666 484 667 430 668 838 669 667 670 488 671 239 672 378 673 459 674 622 675 627 676 437 677 380 678 818 679 461 680 496 681 669 682 679 683 724 684 841 685 629 686 351 687 467 688 438 689 737 690 251 691 462 692 442 693 441 694 469 695 247 696 683 697 842 698 738 699 899 700 670 701 783 702 849 703 820 704 728 705 928 706 791 707 367 708 901 709 630 710 685 711 844 712 633 713 711 714 253 715 691 716 824 717 902 718 686 719 740 720 850 721 375 722 444 723 470 724 483 725 415 726 485 727 905 728 795 729 473 730 634 731 744 732 852 733 960 734 865 735 693 736 797 737 906 738 715 739 807 740 474 741 636 742 694 743 254 744 717 745 575 746 913 747 798 748 811 749 379 750 697 751 431 752 607 753 489 754 866 755 723 756 486 757 908 758 718 759 813 760 476 761 856 762 839 763 725 764 698 765 914 766 752 767 868 768 819 769 814 770 439 771 929 772 490 773 623 774 671 775 739 776 916 777 463 778 843 779 381 780 497 781 930 782 821 783 726 784 961 785 872 786 492 787 631 788 729 789 700 790 443 791 741 792 845 793 920 794 382 795 822 796 851 797 730 798 498 799 880 800 742 801 445 802 471 803 635 804 932 805 687 806 903 807 825 808 500 809 846 810 745 811 826 812 732 813 446 814 962 815 936 816 475 817 853 818 867 819 637 820 907 821 487 822 695 823 746 824 828 825 753 826 854 827 857 828 504 829 799 830 255 831 964 832 909 833 719 834 477 835 915 836 638 837 748 838 944 839 869 840 491 841 699 842 754 843 858 844 478 845 968 846 383 847 910 848 815 849 976 850 870 851 917 852 727 853 493 854 873 855 701 856 931 857 756 858 860 859 499 860 731 861 823 862 922 863 874 864 918 865 502 866 933 867 743 868 760 869 881 870 494 871 702 872 921 873 501 874 876 875 847 876 992 877 447 878 733 879 827 880 934 881 882 882 937 883 963 884 747 885 505 886 855 887 924 888 734 889 829 890 965 891 938 892 884 893 506 894 749 895 945 896 966 897 755 898 859 899 940 900 830 901 911 902 871 903 639 904 888 905 479 906 946 907 750 908 969 909 508 910 861 911 757 912 970 913 919 914 875 915 862 916 758 917 948 918 977 919 923 920 972 921 761 922 877 923 952 924 495 925 703 926 935 927 978 928 883 929 762 930 503 931 925 932 878 933 735 934 993 935 885 936 939 937 994 938 980 939 926 940 764 941 941 942 967 943 886 944 831 945 947 946 507 947 889 948 984 949 751 950 942 951 996 952 971 953 890 954 509 955 949 956 973 957 1000 958 892 959 950 960 863 961 759 962 1008 963 510 964 979 965 953 966 763 967 974 968 954 969 879 970 981 971 982 972 927 973 995 974 765 975 956 976 887 977 985 978 997 979 986 980 943 981 891 982 998 983 766 984 511 985 988 986 1001 987 951 988 1002 989 893 990 975 991 894 992 1009 993 955 994 1004 995 1010 996 957 997 983 998 958 999 987 1000 1012 1001 999 1002 1016 1003 767 1004 989 1005 1003 1006 990 1007 1005 1008 959 1009 1011 1010 1013 1011 895 1012 1006 1013 1014 1014 1017 1015 1018 1016 991 1017 1020 1018 1007 1019 1015 1020 1019 1021 1021 1022 1022 1023 1023
2. The method according to claim 1, wherein the sequence numbers of the Nmax polarized channels are arranged in the second sequence based on reliability of the Nmax polarized channels.
3. The method according to claim 1, wherein ordering of the sequence numbers of the polarized channels in the first sequence is consistent with ordering of sequence numbers less than N in the sequence numbers of the polarized channels in the second sequence.
4. The method according to claim 1, wherein the sequence numbers of the K polarized channels are selected based on reliability of the N polarized channels.
5. The method according to claim 1, wherein the first sequence is pre-stored.
6. The method according to claim 1, wherein the K to-be-encoded bits comprise a cyclic redundancy check (CRC) bit.
7. The method according to claim 1, wherein the K to-be-encoded bits comprise a parity check (PC) bit.
8. The method according to claim 1, wherein after performing the polar code encoding on the to-be-encoded bits, the encoding apparatus performs, based on a target code length, rate matching on the bit sequence after encoding, wherein the outputting the bit sequence after encoding to a receiving device comprises outputting the bit sequence after rate matching to a receiving device.
9. A polar code encoding apparatus, comprising:
a memory storage comprising instructions; and
a processor in communication with the memory, wherein the processor is configured to execute the instructions to perform the steps:
obtaining a first sequence used to encode K to-be-encoded bits, the first sequence comprising sequence numbers of N polarized channels, wherein the first sequence is same as a second sequence or a subset of the second sequence, the second sequence comprises sequence numbers of Nmax polarized channels, K is a positive integer, N=2n, n is a positive integer, n is equal to or greater than 5, K≤N, and Nmax=1024;
selecting sequence numbers of K polarized channels from the first sequence;
performing polar code encoding on the K to-be-encoded bits based on the selected sequence numbers of the K polarized channels, to obtain a bit sequence after encoding; and
outputting, by the encoding apparatus, the bit sequence after encoding to a receiving device;
wherein the second sequence is the sequence shown in Sequence Q11 or Table Q11;
the Sequence Q11 comprising:
[0, 1, 2, 4, 8, 16, 32, 3, 5, 64, 9, 6, 17, 10, 18, 128, 12, 33, 65, 20, 256, 34, 24, 36, 7, 129, 66, 512, 11, 40, 68, 130, 19, 13, 48, 14, 72, 257, 21, 132, 35, 258, 26, 513, 80, 37, 25, 22, 136, 260, 264, 38, 514, 96, 67, 41, 144, 28, 69, 42, 516, 49, 74, 272, 160, 520, 288, 528, 192, 544, 70, 44, 131, 81, 50, 73, 15, 320, 133, 52, 23, 134, 384, 76, 137, 82, 56, 27, 97, 39, 259, 84, 138, 145, 261, 29, 43, 98, 515, 88, 140, 30, 146, 71, 262, 265, 161, 576, 45, 100, 640, 51, 148, 46, 75, 266, 273, 517, 104, 162, 53, 193, 152, 77, 164, 768, 268, 274, 518, 54, 83, 57, 521, 112, 135, 78, 289, 194, 85, 276, 522, 58, 168, 139, 99, 86, 60, 280, 89, 290, 529, 524, 196, 141, 101, 147, 176, 142, 530, 321, 31, 200, 90, 545, 292, 322, 532, 263, 149, 102, 105, 304, 296, 163, 92, 47, 267, 385, 546, 324, 208, 386, 150, 153, 165, 106, 55, 328, 536, 577, 548, 113, 154, 79, 269, 108, 578, 224, 166, 519, 552, 195, 270, 641, 523, 275, 580, 291, 59, 169, 560, 114, 277, 156, 87, 197, 116, 170, 61, 531, 525, 642, 281, 278, 526, 177, 293, 388, 91, 584, 769, 198, 172, 120, 201, 336, 62, 282, 143, 103, 178, 294, 93, 644, 202, 592, 323, 392, 297, 770, 107, 180, 151, 209, 284, 648, 94, 204, 298, 400, 608, 352, 325, 533, 155, 210, 305, 547, 300, 109, 184, 534, 537, 115, 167, 225, 326, 306, 772, 157, 656, 329, 110, 117, 212, 171, 776, 330, 226, 549, 538, 387, 308, 216, 416, 271, 279, 158, 337, 550, 672, 118, 332, 579, 540, 389, 173, 121, 553, 199, 784, 179, 228, 338, 312, 704, 390, 174, 554, 581, 393, 283, 122, 448, 353, 561, 203, 63, 340, 394, 527, 582, 556, 181, 295, 285, 232, 124, 205, 182, 643, 562, 286, 585, 299, 354, 211, 401, 185, 396, 344, 586, 645, 593, 535, 240, 206, 95, 327, 564, 800, 402, 356, 307, 301, 417, 213, 568, 832, 588, 186, 646, 404, 227, 896, 594, 418, 302, 649, 771, 360, 539, 111, 331, 214, 309, 188, 449, 217, 408, 609, 596, 551, 650, 229, 159, 420, 310, 541, 773, 610, 657, 333, 119, 600, 339, 218, 368, 652, 230, 391, 313, 450, 542, 334, 233, 555, 774, 175, 123, 658, 612, 341, 777, 220, 314, 424, 395, 673, 583, 355, 287, 183, 234, 125, 557, 660, 616, 342, 316, 241, 778, 563, 345, 452, 397, 403, 207, 674, 558, 785, 432, 357, 187, 236, 664, 624, 587, 780, 705, 126, 242, 565, 398, 346, 456, 358, 405, 303, 569, 244, 595, 189, 566, 676, 361, 706, 589, 215, 786, 647, 348, 419, 406, 464, 680, 801, 362, 590, 409, 570, 788, 597, 572, 219, 311, 708, 598, 601, 651, 421, 792, 802, 611, 602, 410, 231, 688, 653, 248, 369, 190, 364, 654, 659, 335, 480, 315, 221, 370, 613, 422, 425, 451, 614, 543, 235, 412, 343, 372, 775, 317, 222, 426, 453, 237, 559, 833, 804, 712, 834, 661, 808, 779, 617, 604, 433, 720, 816, 836, 347, 897, 243, 662, 454, 318, 675, 618, 898, 781, 376, 428, 665, 736, 567, 840, 625, 238, 359, 457, 399, 787, 591, 678, 434, 677, 349, 245, 458, 666, 620, 363, 127, 191, 782, 407, 436, 626, 571, 465, 681, 246, 707, 350, 599, 668, 790, 460, 249, 682, 573, 411, 803, 789, 709, 365, 440, 628, 689, 374, 423, 466, 793, 250, 371, 481, 574, 413, 603, 366, 468, 655, 900, 805, 615, 684, 710, 429, 794, 252, 373, 605, 848, 690, 713, 632, 482, 806, 427, 904, 414, 223, 663, 692, 835, 619, 472, 455, 796, 809, 714, 721, 837, 716, 864, 810, 606, 912, 722, 696, 377, 435, 817, 319, 621, 812, 484, 430, 838, 667, 488, 239, 378, 459, 622, 627, 437, 380, 818, 461, 496, 669, 679, 724, 841, 629, 351, 467, 438, 737, 251, 462, 442, 441, 469, 247, 683, 842, 738, 899, 670, 783, 849, 820, 728, 928, 791, 367, 901, 630, 685, 844, 633, 711, 253, 691, 824, 902, 686, 740, 850, 375, 444, 470, 483, 415, 485, 905, 795, 473, 634, 744, 852, 960, 865, 693, 797, 906, 715, 807, 474, 636, 694, 254, 717, 575, 913, 798, 811, 379, 697, 431, 607, 489, 866, 723, 486, 908, 718, 813, 476, 856, 839, 725, 698, 914, 752, 868, 819, 814, 439, 929, 490, 623, 671, 739, 916, 463, 843, 381, 497, 930, 821, 726, 961, 872, 492, 631, 729, 700, 443, 741, 845, 920, 382, 822, 851, 730, 498, 880, 742, 445, 471, 635, 932, 687, 903, 825, 500, 846, 745, 826, 732, 446, 962, 936, 475, 853, 867, 637, 907, 487, 695, 746, 828, 753, 854, 857, 504, 799, 255, 964, 909, 719, 477, 915, 638, 748, 944, 869, 491, 699, 754, 858, 478, 968, 383, 910, 815, 976, 870, 917, 727, 493, 873, 701, 931, 756, 860, 499, 731, 823, 922, 874, 918, 502, 933, 743, 760, 881, 494, 702, 921, 501, 876, 847, 992, 447, 733, 827, 934, 882, 937, 963, 747, 505, 855, 924, 734, 829, 965, 938, 884, 506, 749, 945, 966, 755, 859, 940, 830, 911, 871, 639, 888, 479, 946, 750, 969, 508, 861, 757, 970, 919, 875, 862, 758, 948, 977, 923, 972, 761, 877, 952, 495, 703, 935, 978, 883, 762, 503, 925, 878, 735, 993, 885, 939, 994, 980, 926, 764, 941, 967, 886, 831, 947, 507, 889, 984, 751, 942, 996, 971, 890, 509, 949, 973, 1000, 892, 950, 863, 759, 1008, 510, 979, 953, 763, 974, 954, 879, 981, 982, 927, 995, 765, 956, 887, 985, 997, 986, 943, 891, 998, 766, 511, 988, 1001, 951, 1002, 893, 975, 894, 1009, 955, 1004, 1010, 957, 983, 958, 987, 1012, 999, 1016, 767, 989, 1003, 990, 1005, 959, 1011, 1013, 895, 1006, 1014, 1017, 1018, 991, 1020, 1007, 1015, 1019, 1021, 1022, 1023];
the Table Q11 comprising:
Reliability or sequence Polarized channel number of reliability sequence number 0 0 1 1 2 2 3 4 4 8 5 16 6 32 7 3 8 5 9 64 10 9 11 6 12 17 13 10 14 18 15 128 16 12 17 33 18 65 19 20 20 256 21 34 22 24 23 36 24 7 25 129 26 66 27 512 28 11 29 40 30 68 31 130 32 19 33 13 34 48 35 14 36 72 37 257 38 21 39 132 40 35 41 258 42 26 43 513 44 80 45 37 46 25 47 22 48 136 49 260 50 264 51 38 52 514 53 96 54 67 55 41 56 144 57 28 58 69 59 42 60 516 61 49 62 74 63 272 64 160 65 520 66 288 67 528 68 192 69 544 70 70 71 44 72 131 73 81 74 50 75 73 76 15 77 320 78 133 79 52 80 23 81 134 82 384 83 76 84 137 85 82 86 56 87 27 88 97 89 39 90 259 91 84 92 138 93 145 94 261 95 29 96 43 97 98 98 515 99 88 100 140 101 30 102 146 103 71 104 262 105 265 106 161 107 576 108 45 109 100 110 640 111 51 112 148 113 46 114 75 115 266 116 273 117 517 118 104 119 162 120 53 121 193 122 152 123 77 124 164 125 768 126 268 127 274 128 518 129 54 130 83 131 57 132 521 133 112 134 135 135 78 136 289 137 194 138 85 139 276 140 522 141 58 142 168 143 139 144 99 145 86 146 60 147 280 148 89 149 290 150 529 151 524 152 196 153 141 154 101 155 147 156 176 157 142 158 530 159 321 160 31 161 200 162 90 163 545 164 292 165 322 166 532 167 263 168 149 169 102 170 105 171 304 172 296 173 163 174 92 175 47 176 267 177 385 178 546 179 324 180 208 181 386 182 150 183 153 184 165 185 106 186 55 187 328 188 536 189 577 190 548 191 113 192 154 193 79 194 269 195 108 196 578 197 224 198 166 199 519 200 552 201 195 202 270 203 641 204 523 205 275 206 580 207 291 208 59 209 169 210 560 211 114 212 277 213 156 214 87 215 197 216 116 217 170 218 61 219 531 220 525 221 642 222 281 223 278 224 526 225 177 226 293 227 388 228 91 229 584 230 769 231 198 232 172 233 120 234 201 235 336 236 62 237 282 238 143 239 103 240 178 241 294 242 93 243 644 244 202 245 592 246 323 247 392 248 297 249 770 250 107 251 180 252 151 253 209 254 284 255 648 256 94 257 204 258 298 259 400 260 608 261 352 262 325 263 533 264 155 265 210 266 305 267 547 268 300 269 109 270 184 271 534 272 537 273 115 274 167 275 225 276 326 277 306 278 772 279 157 280 656 281 329 282 110 283 117 284 212 285 171 286 776 287 330 288 226 289 549 290 538 291 387 292 308 293 216 294 416 295 271 296 279 297 158 298 337 299 550 300 672 301 118 302 332 303 579 304 540 305 389 306 173 307 121 308 553 309 199 310 784 311 179 312 228 313 338 314 312 315 704 316 390 317 174 318 554 319 581 320 393 321 283 322 122 323 448 324 353 325 561 326 203 327 63 328 340 329 394 330 527 331 582 332 556 333 181 334 295 335 285 336 232 337 124 338 205 339 182 340 643 341 562 342 286 343 585 344 299 345 354 346 211 347 401 348 185 349 396 350 344 351 586 352 645 353 593 354 535 355 240 356 206 357 95 358 327 359 564 360 800 361 402 362 356 363 307 364 301 365 417 366 213 367 568 368 832 369 588 370 186 371 646 372 404 373 227 374 896 375 594 376 418 377 302 378 649 379 771 380 360 381 539 382 111 383 331 384 214 385 309 386 188 387 449 388 217 389 408 390 609 391 596 392 551 393 650 394 229 395 159 396 420 397 310 398 541 399 773 400 610 401 657 402 333 403 119 404 600 405 339 406 218 407 368 408 652 409 230 410 391 411 313 412 450 413 542 414 334 415 233 416 555 417 774 418 175 419 123 420 658 421 612 422 341 423 777 424 220 425 314 426 424 427 395 428 673 429 583 430 355 431 287 432 183 433 234 434 125 435 557 436 660 437 616 438 342 439 316 440 241 441 778 442 563 443 345 444 452 445 397 446 403 447 207 448 674 449 558 450 785 451 432 452 357 453 187 454 236 455 664 456 624 457 587 458 780 459 705 460 126 461 242 462 565 463 398 464 346 465 456 466 358 467 405 468 303 469 569 470 244 471 595 472 189 473 566 474 676 475 361 476 706 477 589 478 215 479 786 480 647 481 348 482 419 483 406 484 464 485 680 486 801 487 362 488 590 489 409 490 570 491 788 492 597 493 572 494 219 495 311 496 708 497 598 498 601 499 651 500 421 501 792 502 802 503 611 504 602 505 410 506 231 507 688 508 653 509 248 510 369 511 190 512 364 513 654 514 659 515 335 516 480 517 315 518 221 519 370 520 613 521 422 522 425 523 451 524 614 525 543 526 235 527 412 528 343 529 372 530 775 531 317 532 222 533 426 534 453 535 237 536 559 537 833 538 804 539 712 540 834 541 661 542 808 543 779 544 617 545 604 546 433 547 720 548 816 549 836 550 347 551 897 552 243 553 662 554 454 555 318 556 675 557 618 558 898 559 781 560 376 561 428 562 665 563 736 564 567 565 840 566 625 567 238 568 359 569 457 570 399 571 787 572 591 573 678 574 434 575 677 576 349 577 245 578 458 579 666 580 620 581 363 582 127 583 191 584 782 585 407 586 436 587 626 588 571 589 465 590 681 591 246 592 707 593 350 594 599 595 668 596 790 597 460 598 249 599 682 600 573 601 411 602 803 603 789 604 709 605 365 606 440 607 628 608 689 609 374 610 423 611 466 612 793 613 250 614 371 615 481 616 574 617 413 618 603 619 366 620 468 621 655 622 900 623 805 624 615 625 684 626 710 627 429 628 794 629 252 630 373 631 605 632 848 633 690 634 713 635 632 636 482 637 806 638 427 639 904 640 414 641 223 642 663 643 692 644 835 645 619 646 472 647 455 648 796 649 809 650 714 651 721 652 837 653 716 654 864 655 810 656 606 657 912 658 722 659 696 660 377 661 435 662 817 663 319 664 621 665 812 666 484 667 430 668 838 669 667 670 488 671 239 672 378 673 459 674 622 675 627 676 437 677 380 678 818 679 461 680 496 681 669 682 679 683 724 684 841 685 629 686 351 687 467 688 438 689 737 690 251 691 462 692 442 693 441 694 469 695 247 696 683 697 842 698 738 699 899 700 670 701 783 702 849 703 820 704 728 705 928 706 791 707 367 708 901 709 630 710 685 711 844 712 633 713 711 714 253 715 691 716 824 717 902 718 686 719 740 720 850 721 375 722 444 723 470 724 483 725 415 726 485 727 905 728 795 729 473 730 634 731 744 732 852 733 960 734 865 735 693 736 797 737 906 738 715 739 807 740 474 741 636 742 694 743 254 744 717 745 575 746 913 747 798 748 811 749 379 750 697 751 431 752 607 753 489 754 866 755 723 756 486 757 908 758 718 759 813 760 476 761 856 762 839 763 725 764 698 765 914 766 752 767 868 768 819 769 814 770 439 771 929 772 490 773 623 774 671 775 739 776 916 777 463 778 843 779 381 780 497 781 930 782 821 783 726 784 961 785 872 786 492 787 631 788 729 789 700 790 443 791 741 792 845 793 920 794 382 795 822 796 851 797 730 798 498 799 880 800 742 801 445 802 471 803 635 804 932 805 687 806 903 807 825 808 500 809 846 810 745 811 826 812 732 813 446 814 962 815 936 816 475 817 853 818 867 819 637 820 907 821 487 822 695 823 746 824 828 825 753 826 854 827 857 828 504 829 799 830 255 831 964 832 909 833 719 834 477 835 915 836 638 837 748 838 944 839 869 840 491 841 699 842 754 843 858 844 478 845 968 846 383 847 910 848 815 849 976 850 870 851 917 852 727 853 493 854 873 855 701 856 931 857 756 858 860 859 499 860 731 861 823 862 922 863 874 864 918 865 502 866 933 867 743 868 760 869 881 870 494 871 702 872 921 873 501 874 876 875 847 876 992 877 447 878 733 879 827 880 934 881 882 882 937 883 963 884 747 885 505 886 855 887 924 888 734 889 829 890 965 891 938 892 884 893 506 894 749 895 945 896 966 897 755 898 859 899 940 900 830 901 911 902 871 903 639 904 888 905 479 906 946 907 750 908 969 909 508 910 861 911 757 912 970 913 919 914 875 915 862 916 758 917 948 918 977 919 923 920 972 921 761 922 877 923 952 924 495 925 703 926 935 927 978 928 883 929 762 930 503 931 925 932 878 933 735 934 993 935 885 936 939 937 994 938 980 939 926 940 764 941 941 942 967 943 886 944 831 945 947 946 507 947 889 948 984 949 751 950 942 951 996 952 971 953 890 954 509 955 949 956 973 957 1000 958 892 959 950 960 863 961 759 962 1008 963 510 964 979 965 953 966 763 967 974 968 954 969 879 970 981 971 982 972 927 973 995 974 765 975 956 976 887 977 985 978 997 979 986 980 943 981 891 982 998 983 766 984 511 985 988 986 1001 987 951 988 1002 989 893 990 975 991 894 992 1009 993 955 994 1004 995 1010 996 957 997 983 998 958 999 987 1000 1012 1001 999 1002 1016 1003 767 1004 989 1005 1003 1006 990 1007 1005 1008 959 1009 1011 1010 1013 1011 895 1012 1006 1013 1014 1014 1017 1015 1018 1016 991 1017 1020 1018 1007 1019 1015 1020 1019 1021 1021 1022 1022 1023 1023
10. The apparatus according to claim 9, wherein the sequence numbers of the Nmax polarized channels are arranged in the second sequence based on reliability of the Nmax polarized channels.
11. The apparatus according to claim 9, wherein ordering of the sequence numbers of the polarized channels in the first sequence is consistent with ordering of sequence numbers less than N in the sequence numbers of the polarized channels in the second sequence.
12. The apparatus according to claim 9, wherein the sequence numbers of the K polarized channels are selected based reliability of the N polarized channels.
13. The apparatus according to claim 9, wherein the first sequence is pre-stored.
14. The apparatus according to claim 9, wherein the K to-be-encoded bits comprise a cyclic redundancy check (CRC) bit.
15. The apparatus according to claim 9, wherein the K to-be-encoded bits comprise a parity check (PC) bit.
16. The apparatus according to claim 9, wherein the processor is further configured to execute the instructions to perform: rate matching on the bit sequence after encoding based on a target code length, and output the bit sequence after rate matching to the receiving device.
17. An apparatus, comprising:
an input interface circuit, configured to obtain K to-be-encoded bits;
a logic circuit, configured to:
obtain a first sequence used to encode K to-be-encoded bits, the first sequence comprising sequence numbers of N polarized channels, wherein the first sequence is same as a second sequence or a subset of the second sequence, the second sequence comprises sequence numbers of Nmax polarized channels, K is a positive integer, N=2n, n is a positive integer, n is equal to or greater than 5, K≤N, and Nmax=1024;
select sequence numbers of K polarized channels from the first sequence;
perform polar code encoding on the K to-be-encoded bits based on the selected sequence numbers of the K polarized channels, to obtain a bit sequence after encoding; and
an output interface circuit configured to output the bit sequence after encoding to a receiving device;
wherein the second sequence is the sequence shown in Sequence Q11 or Table Q11;
the Sequence Q11 comprising:
[0, 1, 2, 4, 8, 16, 32, 3, 5, 64, 9, 6, 17, 10, 18, 128, 12, 33, 65, 20, 256, 34, 24, 36, 7, 129, 66, 512, 11, 40, 68, 130, 19, 13, 48, 14, 72, 257, 21, 132, 35, 258, 26, 513, 80, 37, 25, 22, 136, 260, 264, 38, 514, 96, 67, 41, 144, 28, 69, 42, 516, 49, 74, 272, 160, 520, 288, 528, 192, 544, 70, 44, 131, 81, 50, 73, 15, 320, 133, 52, 23, 134, 384, 76, 137, 82, 56, 27, 97, 39, 259, 84, 138, 145, 261, 29, 43, 98, 515, 88, 140, 30, 146, 71, 262, 265, 161, 576, 45, 100, 640, 51, 148, 46, 75, 266, 273, 517, 104, 162, 53, 193, 152, 77, 164, 768, 268, 274, 518, 54, 83, 57, 521, 112, 135, 78, 289, 194, 85, 276, 522, 58, 168, 139, 99, 86, 60, 280, 89, 290, 529, 524, 196, 141, 101, 147, 176, 142, 530, 321, 31, 200, 90, 545, 292, 322, 532, 263, 149, 102, 105, 304, 296, 163, 92, 47, 267, 385, 546, 324, 208, 386, 150, 153, 165, 106, 55, 328, 536, 577, 548, 113, 154, 79, 269, 108, 578, 224, 166, 519, 552, 195, 270, 641, 523, 275, 580, 291, 59, 169, 560, 114, 277, 156, 87, 197, 116, 170, 61, 531, 525, 642, 281, 278, 526, 177, 293, 388, 91, 584, 769, 198, 172, 120, 201, 336, 62, 282, 143, 103, 178, 294, 93, 644, 202, 592, 323, 392, 297, 770, 107, 180, 151, 209, 284, 648, 94, 204, 298, 400, 608, 352, 325, 533, 155, 210, 305, 547, 300, 109, 184, 534, 537, 115, 167, 225, 326, 306, 772, 157, 656, 329, 110, 117, 212, 171, 776, 330, 226, 549, 538, 387, 308, 216, 416, 271, 279, 158, 337, 550, 672, 118, 332, 579, 540, 389, 173, 121, 553, 199, 784, 179, 228, 338, 312, 704, 390, 174, 554, 581, 393, 283, 122, 448, 353, 561, 203, 63, 340, 394, 527, 582, 556, 181, 295, 285, 232, 124, 205, 182, 643, 562, 286, 585, 299, 354, 211, 401, 185, 396, 344, 586, 645, 593, 535, 240, 206, 95, 327, 564, 800, 402, 356, 307, 301, 417, 213, 568, 832, 588, 186, 646, 404, 227, 896, 594, 418, 302, 649, 771, 360, 539, 111, 331, 214, 309, 188, 449, 217, 408, 609, 596, 551, 650, 229, 159, 420, 310, 541, 773, 610, 657, 333, 119, 600, 339, 218, 368, 652, 230, 391, 313, 450, 542, 334, 233, 555, 774, 175, 123, 658, 612, 341, 777, 220, 314, 424, 395, 673, 583, 355, 287, 183, 234, 125, 557, 660, 616, 342, 316, 241, 778, 563, 345, 452, 397, 403, 207, 674, 558, 785, 432, 357, 187, 236, 664, 624, 587, 780, 705, 126, 242, 565, 398, 346, 456, 358, 405, 303, 569, 244, 595, 189, 566, 676, 361, 706, 589, 215, 786, 647, 348, 419, 406, 464, 680, 801, 362, 590, 409, 570, 788, 597, 572, 219, 311, 708, 598, 601, 651, 421, 792, 802, 611, 602, 410, 231, 688, 653, 248, 369, 190, 364, 654, 659, 335, 480, 315, 221, 370, 613, 422, 425, 451, 614, 543, 235, 412, 343, 372, 775, 317, 222, 426, 453, 237, 559, 833, 804, 712, 834, 661, 808, 779, 617, 604, 433, 720, 816, 836, 347, 897, 243, 662, 454, 318, 675, 618, 898, 781, 376, 428, 665, 736, 567, 840, 625, 238, 359, 457, 399, 787, 591, 678, 434, 677, 349, 245, 458, 666, 620, 363, 127, 191, 782, 407, 436, 626, 571, 465, 681, 246, 707, 350, 599, 668, 790, 460, 249, 682, 573, 411, 803, 789, 709, 365, 440, 628, 689, 374, 423, 466, 793, 250, 371, 481, 574, 413, 603, 366, 468, 655, 900, 805, 615, 684, 710, 429, 794, 252, 373, 605, 848, 690, 713, 632, 482, 806, 427, 904, 414, 223, 663, 692, 835, 619, 472, 455, 796, 809, 714, 721, 837, 716, 864, 810, 606, 912, 722, 696, 377, 435, 817, 319, 621, 812, 484, 430, 838, 667, 488, 239, 378, 459, 622, 627, 437, 380, 818, 461, 496, 669, 679, 724, 841, 629, 351, 467, 438, 737, 251, 462, 442, 441, 469, 247, 683, 842, 738, 899, 670, 783, 849, 820, 728, 928, 791, 367, 901, 630, 685, 844, 633, 711, 253, 691, 824, 902, 686, 740, 850, 375, 444, 470, 483, 415, 485, 905, 795, 473, 634, 744, 852, 960, 865, 693, 797, 906, 715, 807, 474, 636, 694, 254, 717, 575, 913, 798, 811, 379, 697, 431, 607, 489, 866, 723, 486, 908, 718, 813, 476, 856, 839, 725, 698, 914, 752, 868, 819, 814, 439, 929, 490, 623, 671, 739, 916, 463, 843, 381, 497, 930, 821, 726, 961, 872, 492, 631, 729, 700, 443, 741, 845, 920, 382, 822, 851, 730, 498, 880, 742, 445, 471, 635, 932, 687, 903, 825, 500, 846, 745, 826, 732, 446, 962, 936, 475, 853, 867, 637, 907, 487, 695, 746, 828, 753, 854, 857, 504, 799, 255, 964, 909, 719, 477, 915, 638, 748, 944, 869, 491, 699, 754, 858, 478, 968, 383, 910, 815, 976, 870, 917, 727, 493, 873, 701, 931, 756, 860, 499, 731, 823, 922, 874, 918, 502, 933, 743, 760, 881, 494, 702, 921, 501, 876, 847, 992, 447, 733, 827, 934, 882, 937, 963, 747, 505, 855, 924, 734, 829, 965, 938, 884, 506, 749, 945, 966, 755, 859, 940, 830, 911, 871, 639, 888, 479, 946, 750, 969, 508, 861, 757, 970, 919, 875, 862, 758, 948, 977, 923, 972, 761, 877, 952, 495, 703, 935, 978, 883, 762, 503, 925, 878, 735, 993, 885, 939, 994, 980, 926, 764, 941, 967, 886, 831, 947, 507, 889, 984, 751, 942, 996, 971, 890, 509, 949, 973, 1000, 892, 950, 863, 759, 1008, 510, 979, 953, 763, 974, 954, 879, 981, 982, 927, 995, 765, 956, 887, 985, 997, 986, 943, 891, 998, 766, 511, 988, 1001, 951, 1002, 893, 975, 894, 1009, 955, 1004, 1010, 957, 983, 958, 987, 1012, 999, 1016, 767, 989, 1003, 990, 1005, 959, 1011, 1013, 895, 1006, 1014, 1017, 1018, 991, 1020, 1007, 1015, 1019, 1021, 1022, 1023];
the Table Q11 comprising:
Reliability or sequence Polarized channel number of reliability sequence number 0 0 1 1 2 2 3 4 4 8 5 16 6 32 7 3 8 5 9 64 10 9 11 6 12 17 13 10 14 18 15 128 16 12 17 33 18 65 19 20 20 256 21 34 22 24 23 36 24 7 25 129 26 66 27 512 28 11 29 40 30 68 31 130 32 19 33 13 34 48 35 14 36 72 37 257 38 21 39 132 40 35 41 258 42 26 43 513 44 80 45 37 46 25 47 22 48 136 49 260 50 264 51 38 52 514 53 96 54 67 55 41 56 144 57 28 58 69 59 42 60 516 61 49 62 74 63 272 64 160 65 520 66 288 67 528 68 192 69 544 70 70 71 44 72 131 73 81 74 50 75 73 76 15 77 320 78 133 79 52 80 23 81 134 82 384 83 76 84 137 85 82 86 56 87 27 88 97 89 39 90 259 91 84 92 138 93 145 94 261 95 29 96 43 97 98 98 515 99 88 100 140 101 30 102 146 103 71 104 262 105 265 106 161 107 576 108 45 109 100 110 640 111 51 112 148 113 46 114 75 115 266 116 273 117 517 118 104 119 162 120 53 121 193 122 152 123 77 124 164 125 768 126 268 127 274 128 518 129 54 130 83 131 57 132 521 133 112 134 135 135 78 136 289 137 194 138 85 139 276 140 522 141 58 142 168 143 139 144 99 145 86 146 60 147 280 148 89 149 290 150 529 151 524 152 196 153 141 154 101 155 147 156 176 157 142 158 530 159 321 160 31 161 200 162 90 163 545 164 292 165 322 166 532 167 263 168 149 169 102 170 105 171 304 172 296 173 163 174 92 175 47 176 267 177 385 178 546 179 324 180 208 181 386 182 150 183 153 184 165 185 106 186 55 187 328 188 536 189 577 190 548 191 113 192 154 193 79 194 269 195 108 196 578 197 224 198 166 199 519 200 552 201 195 202 270 203 641 204 523 205 275 206 580 207 291 208 59 209 169 210 560 211 114 212 277 213 156 214 87 215 197 216 116 217 170 218 61 219 531 220 525 221 642 222 281 223 278 224 526 225 177 226 293 227 388 228 91 229 584 230 769 231 198 232 172 233 120 234 201 235 336 236 62 237 282 238 143 239 103 240 178 241 294 242 93 243 644 244 202 245 592 246 323 247 392 248 297 249 770 250 107 251 180 252 151 253 209 254 284 255 648 256 94 257 204 258 298 259 400 260 608 261 352 262 325 263 533 264 155 265 210 266 305 267 547 268 300 269 109 270 184 271 534 272 537 273 115 274 167 275 225 276 326 277 306 278 772 279 157 280 656 281 329 282 110 283 117 284 212 285 171 286 776 287 330 288 226 289 549 290 538 291 387 292 308 293 216 294 416 295 271 296 279 297 158 298 337 299 550 300 672 301 118 302 332 303 579 304 540 305 389 306 173 307 121 308 553 309 199 310 784 311 179 312 228 313 338 314 312 315 704 316 390 317 174 318 554 319 581 320 393 321 283 322 122 323 448 324 353 325 561 326 203 327 63 328 340 329 394 330 527 331 582 332 556 333 181 334 295 335 285 336 232 337 124 338 205 339 182 340 643 341 562 342 286 343 585 344 299 345 354 346 211 347 401 348 185 349 396 350 344 351 586 352 645 353 593 354 535 355 240 356 206 357 95 358 327 359 564 360 800 361 402 362 356 363 307 364 301 365 417 366 213 367 568 368 832 369 588 370 186 371 646 372 404 373 227 374 896 375 594 376 418 377 302 378 649 379 771 380 360 381 539 382 111 383 331 384 214 385 309 386 188 387 449 388 217 389 408 390 609 391 596 392 551 393 650 394 229 395 159 396 420 397 310 398 541 399 773 400 610 401 657 402 333 403 119 404 600 405 339 406 218 407 368 408 652 409 230 410 391 411 313 412 450 413 542 414 334 415 233 416 555 417 774 418 175 419 123 420 658 421 612 422 341 423 777 424 220 425 314 426 424 427 395 428 673 429 583 430 355 431 287 432 183 433 234 434 125 435 557 436 660 437 616 438 342 439 316 440 241 441 778 442 563 443 345 444 452 445 397 446 403 447 207 448 674 449 558 450 785 451 432 452 357 453 187 454 236 455 664 456 624 457 587 458 780 459 705 460 126 461 242 462 565 463 398 464 346 465 456 466 358 467 405 468 303 469 569 470 244 471 595 472 189 473 566 474 676 475 361 476 706 477 589 478 215 479 786 480 647 481 348 482 419 483 406 484 464 485 680 486 801 487 362 488 590 489 409 490 570 491 788 492 597 493 572 494 219 495 311 496 708 497 598 498 601 499 651 500 421 501 792 502 802 503 611 504 602 505 410 506 231 507 688 508 653 509 248 510 369 511 190 512 364 513 654 514 659 515 335 516 480 517 315 518 221 519 370 520 613 521 422 522 425 523 451 524 614 525 543 526 235 527 412 528 343 529 372 530 775 531 317 532 222 533 426 534 453 535 237 536 559 537 833 538 804 539 712 540 834 541 661 542 808 543 779 544 617 545 604 546 433 547 720 548 816 549 836 550 347 551 897 552 243 553 662 554 454 555 318 556 675 557 618 558 898 559 781 560 376 561 428 562 665 563 736 564 567 565 840 566 625 567 238 568 359 569 457 570 399 571 787 572 591 573 678 574 434 575 677 576 349 577 245 578 458 579 666 580 620 581 363 582 127 583 191 584 782 585 407 586 436 587 626 588 571 589 465 590 681 591 246 592 707 593 350 594 599 595 668 596 790 597 460 598 249 599 682 600 573 601 411 602 803 603 789 604 709 605 365 606 440 607 628 608 689 609 374 610 423 611 466 612 793 613 250 614 371 615 481 616 574 617 413 618 603 619 366 620 468 621 655 622 900 623 805 624 615 625 684 626 710 627 429 628 794 629 252 630 373 631 605 632 848 633 690 634 713 635 632 636 482 637 806 638 427 639 904 640 414 641 223 642 663 643 692 644 835 645 619 646 472 647 455 648 796 649 809 650 714 651 721 652 837 653 716 654 864 655 810 656 606 657 912 658 722 659 696 660 377 661 435 662 817 663 319 664 621 665 812 666 484 667 430 668 838 669 667 670 488 671 239 672 378 673 459 674 622 675 627 676 437 677 380 678 818 679 461 680 496 681 669 682 679 683 724 684 841 685 629 686 351 687 467 688 438 689 737 690 251 691 462 692 442 693 441 694 469 695 247 696 683 697 842 698 738 699 899 700 670 701 783 702 849 703 820 704 728 705 928 706 791 707 367 708 901 709 630 710 685 711 844 712 633 713 711 714 253 715 691 716 824 717 902 718 686 719 740 720 850 721 375 722 444 723 470 724 483 725 415 726 485 727 905 728 795 729 473 730 634 731 744 732 852 733 960 734 865 735 693 736 797 737 906 738 715 739 807 740 474 741 636 742 694 743 254 744 717 745 575 746 913 747 798 748 811 749 379 750 697 751 431 752 607 753 489 754 866 755 723 756 486 757 908 758 718 759 813 760 476 761 856 762 839 763 725 764 698 765 914 766 752 767 868 768 819 769 814 770 439 771 929 772 490 773 623 774 671 775 739 776 916 777 463 778 843 779 381 780 497 781 930 782 821 783 726 784 961 785 872 786 492 787 631 788 729 789 700 790 443 791 741 792 845 793 920 794 382 795 822 796 851 797 730 798 498 799 880 800 742 801 445 802 471 803 635 804 932 805 687 806 903 807 825 808 500 809 846 810 745 811 826 812 732 813 446 814 962 815 936 816 475 817 853 818 867 819 637 820 907 821 487 822 695 823 746 824 828 825 753 826 854 827 857 828 504 829 799 830 255 831 964 832 909 833 719 834 477 835 915 836 638 837 748 838 944 839 869 840 491 841 699 842 754 843 858 844 478 845 968 846 383 847 910 848 815 849 976 850 870 851 917 852 727 853 493 854 873 855 701 856 931 857 756 858 860 859 499 860 731 861 823 862 922 863 874 864 918 865 502 866 933 867 743 868 760 869 881 870 494 871 702 872 921 873 501 874 876 875 847 876 992 877 447 878 733 879 827 880 934 881 882 882 937 883 963 884 747 885 505 886 855 887 924 888 734 889 829 890 965 891 938 892 884 893 506 894 749 895 945 896 966 897 755 898 859 899 940 900 830 901 911 902 871 903 639 904 888 905 479 906 946 907 750 908 969 909 508 910 861 911 757 912 970 913 919 914 875 915 862 916 758 917 948 918 977 919 923 920 972 921 761 922 877 923 952 924 495 925 703 926 935 927 978 928 883 929 762 930 503 931 925 932 878 933 735 934 993 935 885 936 939 937 994 938 980 939 926 940 764 941 941 942 967 943 886 944 831 945 947 946 507 947 889 948 984 949 751 950 942 951 996 952 971 953 890 954 509 955 949 956 973 957 1000 958 892 959 950 960 863 961 759 962 1008 963 510 964 979 965 953 966 763 967 974 968 954 969 879 970 981 971 982 972 927 973 995 974 765 975 956 976 887 977 985 978 997 979 986 980 943 981 891 982 998 983 766 984 511 985 988 986 1001 987 951 988 1002 989 893 990 975 991 894 992 1009 993 955 994 1004 995 1010 996 957 997 983 998 958 999 987 1000 1012 1001 999 1002 1016 1003 767 1004 989 1005 1003 1006 990 1007 1005 1008 959 1009 1011 1010 1013 1011 895 1012 1006 1013 1014 1014 1017 1015 1018 1016 991 1017 1020 1018 1007 1019 1015 1020 1019 1021 1021 1022 1022 1023 1023
18. The apparatus according to claim 17, wherein the sequence numbers of the Nmax polarized channels are arranged in the second sequence based on reliability of the Nmax polarized channels.
19. The apparatus according to claim 17, wherein ordering of the sequence numbers of the polarized channels in the first sequence is consistent with ordering of sequence numbers less than N in the sequence numbers of the polarized channels in the second sequence.
20. The apparatus according to claim 18, wherein the sequence numbers of the K polarized channels are selected based on reliability of the N polarized channels.
21. The apparatus according to claim 17, wherein the first sequence is pre-stored.
22. The apparatus according to claim 17, wherein the K to-be-encoded bits comprise a cyclic redundancy check (CRC) bit.
23. The apparatus according to claim 17, wherein the K to-be-encoded bits comprise a parity check (PC) bit.
24. The apparatus according to claim 17, wherein the logic circuit is further configured to rate match on the bit sequence after encoding based on a target code length, and the output interface circuit is configured to output the bit sequence after rate matching to a receiving device.
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